Chapter 7 Review Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Simplify tan(t) sec(t) cos(t) to a single trig function. #2 Points possible: 1. Total attempts: 3 Simplify csc(t) cot(t) to a single trig function. #3 Points possible: 1. Total attempts: 3 Simplify sec(t)cot(t) to a single trig function. #4 Points possible: 1. Total attempts: 3 Simplify cos2 (t) 1 cos2 (t) to an expression involving a single trig function with no fractions. #5 Points possible: 1. Total attempts: 3 Simplify 1 + tan(t) 1 + cot(t) to a single trig function. #6 Points possible: 1. Total attempts: 3 Fill in the blanks: 1. If tan x = 4 then tan( x) = 2. If sin x = 0.1 then sin( x) = 3. If cos x = 0.9 then cos( x)= 4. If tan x = 1 then tan( + x)= #7 Points possible: 1. Total attempts: 3 Simplify to an expression involving a single trigonometric function with no fractions. cot( x)cos( x) + sin( x) #8 Points possible: 1. Total attempts: 3 Simplify and write the trigonometric expression in terms of sine and cosine: tan2 x sec2 x = . #9 Points possible: 1. Total attempts: 3 Determine the value of sin2 x + cos2 x for x = 70 degrees. #10 Points possible: 1. Total attempts: 3 Simplify cos2 (t) sin2 (t) + cos2 (t) to an expression involving a single trig function with no fractions. #11 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to write the expression as a trigonometric function of one number: B 3 2 3 2 cos cos + sin sin = cos = . 7 7 21 21 2 A A= , B= . #12 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to write the expression as a trigonometric function of one number: tan 72 tan 12 = tan A = B. 1 + tan 72 tan 12 A= , B= . #13 Points possible: 1. Total attempts: 3 If sin(x + y) sin(x y) = 2f(x)sin y, then f(x) = . #14 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of sin 165 = A= B= A(B 1) . 4 ; . #15 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of tan 75 = A= B= ; . A + 1 B 1 . #16 Points possible: 1. Total attempts: 3 Rewrite cos(x ) in terms of sin(x) and cos(x). 6 #17 Points possible: 1. Total attempts: 3 19 Use an addition or subtraction formula to find the exact value of sin( ) = 12 A= ; B= . A(B + 1) . 4 #18 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of cos( )= 12 A= ; B= . A(B + 1) 4 #19 Points possible: 1. Total attempts: 3 Find the exact value of cos(105 ). #20 Points possible: 1. Total attempts: 3 Simplify cot( x) to a single trig function using a sum or difference of angles identity. 2 . #21 Points possible: 1. Total attempts: 3 If csc(x) = 3, for 90 < x < 180 , then sin( x )= 2 cos( x )= 2 tan( x )= 2 #22 Points possible: 1. Total attempts: 3 Using a double-angle or half-angle formula to simplify the given expressions. (a) If cos2 (26 ) sin2 (26 ) = cos(A ), then A= degrees (b) If cos2 (9x) sin2 (9x) = cos(B), then B= . #23 Points possible: 1. Total attempts: 3 4 , csc x < 0, then 5 sin 2x = ; cos 2x = ; tan 2x = . If cos x = #24 Points possible: 1. Total attempts: 3 If sin x = sin 2x = cos 2x = tan 2x = 3 , x in quadrant III, then 5 ; ; . #25 Points possible: 1. Total attempts: 3 If tan x = sin(2x) = cos(2x) = tan(2x) = 1 , cos x > 0, , then 3 ; ; . #26 Points possible: 1. Total attempts: 3 Use a half angle formula to fill in the blanks in the identity below: (cos(6x))2 = 1/2 + 1/2 cos( x) 12 #27 Points possible: 1. Total attempts: 3 Use half angle formulas to fill in the blanks in the identity below: (sin(3x))4 = 3/8 1 cos( 2 6 x )+ 1 cos( 8 12 x) #28 Points possible: 1. Total attempts: 3 If sin 15 = A= B= 1 A B, then, by using a half-angle formula, find 2 , . #29 Points possible: 1. Total attempts: 3 If cos 22.5 = A= B= 1 A + B, then, by using a half-angle formula, find 2 , . #30 Points possible: 1. Total attempts: 3 = A B, then, by using a half-angle formula, find 8 A= , B= . If tan #31 Points possible: 1. Total attempts: 3 Solve sin(x) = 0.37 on 0 x < 2. There are two solutions, A and B, with A < B. A= B= Give your answers accurate to 3 decimal places. #32 Points possible: 1. Total attempts: 3 Solve 6 cos(3x) = 2 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas. #33 Points possible: 1. Total attempts: 3 Find all solutions to 2 cos() = 1 on the interval 0 < 2. = Give your answers as exact values in a list separated by commas. #34 Points possible: 1. Total attempts: 3 Solve for t, 0 t < 2. 32 sin(t)cos(t) = 8 cos(t) t= Give your answers as values rounded to at least two decimal places in a list separated by commas. #35 Points possible: 1. Total attempts: 3 Solve 4 cos2 (x) 9 cos(x) + 2 = 0 for all solutions 0 x < 2. x= Give your answers as values accurate to at least two decimal places in a list separated by commas. #36 Points possible: 1. Total attempts: 3 Solve sin2 (x) = 7 cos(x) for all solutions 0 x < 2. x= Give your answers as values accurate to at least two decimal places in a list separated by commas. #37 Points possible: 1. Total attempts: 3 Solve 8 sin(2) 15 cos() = 0 for all solutions 0 < 2. = Give your answers accurate to at least 2 decimal places and in a list separated by commas. #38 Points possible: 1. Total attempts: 3 Solve 2 cos2 (t) + 7 cos(t) + 5 = 0 for all solutions. where k Z t= #39 Points possible: 1. Total attempts: 3 Give the smallest two solutions of sin(2) = 0.0863 on [ 0, 2 ). Separate the two solutions with a comma. #40 Points possible: 1. Total attempts: 3 Solve 12 sin2 (x) 2 cos(x) 10 = 0 for all solutions 0 x < 2 x= Give your answers accurate to 2 decimal places, as a list separated by commas #41 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x y 0 -5 1 -1 2 3 3 -1 4 -5 5 -1 6 3 y= #42 Points possible: 1. Total attempts: 3 A population of rabbits oscillates 19 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 650 rabbits and increases by 140 each year. Find an equation for the population, P, in terms of the months since January, t. P (t) = #43 Points possible: 1. Total attempts: 3 A population of rabbits oscillates 26 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 1000 rabbits and increases by 5% each month. Find an equation for the population, P, in terms of the months since January, t. P (t) = #44 Points possible: 1. Total attempts: 3 A spring is attached to the ceiling and pulled 6 cm down from equilibrium and released. The amplitude decreases by 16% each second. The spring oscillates 8 times each second. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t. D(t) = #45 Points possible: 1. Total attempts: 3 A spring is attached to the ceiling and pulled 20 cm down from equilibrium and released. After 4 seconds the amplitude has decreased to 17 cm. The spring oscillates 11 times each second. Assume that the amplitude is decreasing exponentially. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t. D(t) = #46 Points possible: 1. Total attempts: 3 Find an equation of the form y = abx + c sin( x y 0 6 1 20 To fit the data: a= b= c= 2 54 3 160 x) that fits the data below 2 #47 Points possible: 1. Total attempts: 3 Match each graph with it's equation type: - abx + sin(5x) - (mx + b)sin(5x) - sin(5x) + mx + b - (ab )sin(5x) x a. b. c. d. #48 Points possible: 1. Total attempts: 3 The displacement of a mass suspended by a spring is modeled by the function h(t) = 9 sin(6t) Where h(t) is measured in centimeters, and t is measured in seconds Find the: Amplitude: Period: Frequency: cm seconds Hz #49 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x 0 2 4 6 8 10 12 y -8 -4 0 -4 -8 -4 0 Hint: Plot the points and sketch your own graph if needed. y= #50 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x y y= 0 1 2 4 4 7 6 4 8 1 10 4 12 7 Assignment 7.1 Solving Trigonometric Equations with Identities Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Simplify sec(t) cos(t) sin(t) to a single trig function. #2 Points possible: 1. Total attempts: 3 Simplify cot(t) csc(t) to a single trig function. #3 Points possible: 1. Total attempts: 3 Simplify cos(t)tan(t) to a single trig function. #4 Points possible: 1. Total attempts: 3 Simplify csc2 (t) csc2 (t) 1 to an expression involving a single trig function with no fractions. #5 Points possible: 1. Total attempts: 3 Simplify 1 + cot(t) 1 + tan(t) to a single trig function. #6 Points possible: 1. Total attempts: 3 Fill in the blanks: 1. If tan x = 1 then tan( x) = 2. If sin x = 0.3 then sin( x) = 3. If cos x = 0.4 then cos( x)= 4. If tan x = 1.5 then tan( + x)= #7 Points possible: 1. Total attempts: 3 Simplify to an expression involving a single trigonometric function with no fractions. cot( x)cos( x) + sin( x) #8 Points possible: 1. Total attempts: 3 Simplify and write the trigonometric expression in terms of sine and cosine: tan2 x sec2 x = . #9 Points possible: 1. Total attempts: 3 Determine the value of sin2 x + cos2 x for x = 80 degrees. 1 #10 Points possible: 1. Total attempts: 3 Simplify sin2 (t) + cos2 (t) sin2 (t) to an expression involving a single trig function with no fractions. Assignment 7.2 Sum and Difference Identities Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to write the expression as a trigonometric function of one number: 3 2 3 2 B cos cos + sin sin = cos = . 7 7 21 21 2 A A= 3 , B= 1 . #2 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to write the expression as a trigonometric function of one number: tan 79 tan 19 = tan A = B. 1 + tan 79 tan 19 A = 60 , B= 3 . #3 Points possible: 1. Total attempts: 3 If sin(x + y) sin(x y) = 2f(x)sin y, then f(x) = cos x . #4 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of sin 165 = A= B= ; . A(B 1) . 4 #5 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of tan 75 = A= B= ; . #6 Points possible: 1. Total attempts: 3 Rewrite cos(x + 11 ) in terms of sin(x) and cos(x). 6 A + 1 B 1 . #7 Points possible: 1. Total attempts: 3 19 Use an addition or subtraction formula to find the exact value of sin( ) = 12 A= ; B= . A(B + 1) . 4 #8 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of cos( )= 12 A= ; B= . A(B + 1) 4 #9 Points possible: 1. Total attempts: 3 Find the exact value of sin(255 ). #10 Points possible: 1. Total attempts: 3 Simplify sec( x) to a single trig function using a sum or difference of angles identity. 2 . Assignment 7.3 Double-Angle, Half-Angle, and Reduction Formulas #1 Points possible: 1. Total attempts: 3 If csc(x) = 4, for 90 < x < 180 , then sin( x )= 2 cos( x )= 2 tan( x )= 2 #2 Points possible: 1. Total attempts: 3 Using a double-angle or half-angle formula to simplify the given expressions. (a) If cos2 (25 ) sin2 (25 ) = cos(A ), then A= degrees (b) If cos2 (2x) sin2 (2x) = cos(B), then B= . #3 Points possible: 1. Total attempts: 3 4 , csc x < 0, then 5 sin 2x = ; cos 2x = ; tan 2x = . If cos x = #4 Points possible: 1. Total attempts: 3 If sin x = sin 2x = cos 2x = tan 2x = 3 , x in quadrant III, then 5 ; ; . Name: Syd Hendricks #5 Points possible: 1. Total attempts: 3 If tan x = sin(2x) = cos(2x) = tan(2x) = 1 , cos x > 0, , then 3 ; ; . #6 Points possible: 1. Total attempts: 3 Use a half angle formula to fill in the blanks in the identity below: (cos(2x))2 = + cos( x) #7 Points possible: 1. Total attempts: 3 Use half angle formulas to fill in the blanks in the identity below: 4 (sin(5x)) = 1 cos( 2 x )+ 1 cos( 8 x) #8 Points possible: 1. Total attempts: 3 If sin 15 = A= B= 1 A B, then, by using a half-angle formula, find 2 , . #9 Points possible: 1. Total attempts: 3 If cos 22.5 = A= B= 1 A + B, then, by using a half-angle formula, find 2 , . #10 Points possible: 1. Total attempts: 3 = A B, then, by using a half-angle formula, find 8 A= , B= . If tan Assignment 7.5 Solving Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Solve sin(x) = 0.19 on 0 x < 2. There are two solutions, A and B, with A < B. A= B= Give your answers accurate to 3 decimal places. #2 Points possible: 1. Total attempts: 3 Solve 6 cos(3x) = 3 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas. #3 Points possible: 1. Total attempts: 3 Find all solutions to 2 cos() = 3 on the interval 0 < 2. = Give your answers as exact values in a list separated by commas. #4 Points possible: 1. Total attempts: 3 Solve for t, 0 t < 2. 36 sin(t)cos(t) = 4 sin(t) t= Give your answers as values rounded to at least two decimal places in a list separated by commas. #5 Points possible: 1. Total attempts: 3 Solve 2 cos2 (w) 5 cos(w) + 2 = 0 for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #6 Points possible: 1. Total attempts: 3 Solve cos2 (x) = 8 sin(x) for all solutions 0 x < 2. x= Give your answers as values accurate to at least two decimal places in a list separated by commas. #7 Points possible: 1. Total attempts: 3 Solve 5 sin(2x) 4 sin(x) = 0 for all solutions 0 x < 2. x= Give your answers accurate to at least 2 decimal places and in a list separated by commas. #8 Points possible: 1. Total attempts: 3 Solve 2 cos2 (w) + 7 cos(w) + 5 = 0 for all solutions. w= where k Z #9 Points possible: 1. Total attempts: 3 Give the smallest two solutions of cos(2) = 0.4304 on [ 0, 2 ). Separate the two solutions with a comma. #10 Points possible: 1. Total attempts: 3 Solve 6 sin2 (x) + 5 cos(x) 7 = 0 for all solutions 0 x < 2 x= Give your answers accurate to 2 decimal places, as a list separated by commas Assignment 7.6 Modeling with Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x y 0 -1 2 -4 4 -7 6 -4 8 -1 10 -4 12 -7 y= #2 Points possible: 1. Total attempts: 3 A population of rabbits oscillates 20 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 650 rabbits and increases by 200 each year. Find an equation for the population, P, in terms of the months since January, t. P (t) = #3 Points possible: 1. Total attempts: 3 A population of rabbits oscillates 22 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 900 rabbits and increases by 9% each month. Find an equation for the population, P, in terms of the months since January, t. P (t) = #4 Points possible: 1. Total attempts: 3 A spring is attached to the ceiling and pulled 19 cm down from equilibrium and released. The amplitude decreases by 6% each second. The spring oscillates 14 times each second. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t. D(t) = #5 Points possible: 1. Total attempts: 3 A spring is attached to the ceiling and pulled 14 cm down from equilibrium and released. After 4 seconds the amplitude has decreased to 12 cm. The spring oscillates 8 times each second. Assume that the amplitude is decreasing exponentially. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t. D(t) = #6 Points possible: 1. Total attempts: 3 Find an equation of the form y = abx + c sin( x y 0 4 1 27 2 144 3 861 To fit the data: a= b= c= #7 Points possible: 1. Total attempts: 3 Match each graph with it's equation type: - (abx )sin(5x) - abx + sin(5x) - sin(5x) + mx + b - (mx + b)sin(5x) a. b. c. d. x) that fits the data below 2 #8 Points possible: 1. Total attempts: 3 The displacement of a mass suspended by a spring is modeled by the function h(t) = 15 sin(7t) Where h(t) is measured in centimeters, and t is measured in seconds Find the: Amplitude: Period: Frequency: cm seconds Hz #9 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x 0 4 8 12 16 20 24 y 3 1 3 5 3 1 3 Hint: Plot the points and sketch your own graph if needed. y= #10 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x y y= 0 8 3 4 6 0 9 4 12 8 15 4 18 0 1. (Sec2 t + 1) / Cos t 2. 0. 3. Csc (t) 4. Cos (2t) - Cos (2)t 5. - Tan2 (t) 6. a) - 4 b) - 1 c) 0.9 d) 1 7. - Sin (x) - Cos (x) Cot (x) 8. (Sin2 / Cos2 ) - (1 / Cos2 ) 9. 1 10. Cos2 t 11. A = 3, B=1 12. B = 7.74597 13. f (x) = Cos (x) 14. A = 2, B = 3 15. A = 3 B=3 16. 3/2 Cos x + Sin x 17. A = 6 B=2 18. A = -2 B=6 19. - 0.25882 20. Sec2 x 21. a) 0.169102 b) 0.985599 c) 0.1715729 22. a) 52 b) 18 23. a) 0.96 b) 0.21799999 c) - 3.42857 24. Sin 2x = - 0.96 Cos 2x = - 0. 28 Tan 2x = 3.42857 25. Sin 2x = - 0.6 Cos 2x = 0.80 Tan 2x = - 0.75 26. , , 12 27. 3/8, 6, 12 28. A = 2, B = 3 29. A = 2, B = 2 30. A = 2, B = 2 31. A = 21.716, B = 158.28 32. X =23.51, 336.49 33. /3, 2/3, 4/3 34. t = 2n - Sin-1 (1/4) 35. x = - 1 .12581, 1.65472, 4.13820 36. x = - 6.77733, - 5.51010, -1.38933, 1.80785, 4.14397 37. = (n + Tan-1 (1/15 (16 - 31)) 38. t = 2.05943, 4.5366, 7.65662, 11.7466, 13.1276 39. = n + Sin-1 (0.863) 40. x = 1.01341 41. y = 4 Sin (2(X - 2)) - 1 42. 19 Sin (/ 70) + 650 43. - 26 Cos (/6 ) + 1000 (0.05)t 44. 6 (1 - 0.16)t Cos (16t) + avg 45. 20 (0.92195)t Cos (22t) + avg 46. a) 160. b) 3 c) 1 47. Graph 1. C) 2. a) 3. d) 4. b) 48. Amplitude = 9 Period = 6.283 Frequency = 0.15915 49. - 4 Sin (/ 4 - 4) - 4 50. 4 Sin ((/ 4 - 4) + 3. ***END*** 1. (1 /Cos (t)) ((1/ Cos t ) - Cos t) 2. Cos t 3. Sin t 4. Sec2 t 5. 1 6. a) - 1 b) - 0.3 c) 0.4 d) - 1.57. 7. - Sin (x) - Cos (x) Cot (x) 8. (Sin2 - 1) / (Cos2 ) 9. 1 10. Csc2 (t) ***END*** 1. A = 3, B =1 2. A = 60, B = 3 3. f (x) = Cos x 4. A = 6, B = 2 5. A = 3, B = 3 6. = 3/2 Cos (x) + Sin x 7. A = 6, B = 2 8. A = - 2, B= 6 9. - 0.50639 10. Csc (x) ***END*** 1. a) 0.126 b) - 0.992 c) - 0.127 2. a) A = 50 b) B = 4x 3. a) - 0.96 b) 0.28 c) - 3.42857 4. a) - 0.96 b) 0.28 c) 3.42857 5. a) - 0.6 b) 0.8 c) 0.75 6. , , 4 7. 20, 5 , 5 8. A = 2, B = 3 9. A = 2, B = 2 10. A = 2, B= 2. ***END*** 1. A = 10.95278 B = 169.0472 2. x = (5 + 6n) / 9, x = ( + 6n) /9 3. = /6 + 2n, = 11/6 + 2n 4. t= 2n + 1.45946, t= 2n, t= + 2n, t= 2n - 1.45946 5. w= 2/3 + 2n, w= /3 + 2n 6. x = 2n - 0.12342, x = 2n + n - (-0.12342) 7. x= 2n + 1.5928, x = 2n, x= + 2n, x = 2n - 1.15928 8. w= + 2n 9. = (2n + 1.12586), = (2n - 1.12586) 10. X = 0.463121 ***END*** 1. y = -4 Sin (/4x - 4) -4 2. p(t) = 20 (Sin t) + 650 3. p(t) = -22 Cos(/6t) + 900 (1.09)t 4. D(t) = 19 Cos (/7t) + 14 (-1.06)t 5. D(t) = 14 (Sin t) +850 6. D(t) = 10 (0.92582)t Cos (/4t0 + 14 7. Graph 1. (d) Graph 2. (b) Graph 3. (c) Graph 4. (a) 8. Amplitude = 15 Period = 21.995 Frequency = 0.04547 9. y = -4 Sin (/4x - 4) -4 10. y = 4 Sin (/6x - 6) 4 ***END*** Assignment 7.5 Solving Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Solve sin(x) = 0.39 on 0 x < 2. There are two solutions, A and B, with A < B. A= B= Give your answers accurate to 3 decimal places. #2 Points possible: 1. Total attempts: 3 Solve 4 cos(3x) = 3 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas. #3 Points possible: 1. Total attempts: 3 Find all solutions to 2 cos() = 3 on the interval 0 < 2. = Give your answers as exact values in a list separated by commas. #4 Points possible: 1. Total attempts: 3 Solve for t, 0 t < 2. 20 sin(t)cos(t) = 12 cos(t) t= Give your answers as values rounded to at least two decimal places in a list separated by commas. #5 Points possible: 1. Total attempts: 3 Solve 2 cos2 (w) 5 cos(w) + 2 = 0 for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #6 Points possible: 1. Total attempts: 3 Solve sin2 (w) = 6 cos(w) for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #7 Points possible: 1. Total attempts: 3 Solve 7 sin(2) + 5 sin() = 0 for all solutions 0 < 2. = Give your answers accurate to at least 2 decimal places and in a list separated by commas. #8 Points possible: 1. Total attempts: 3 Solve 2 cos2 (x) cos(x) 3 = 0 for all solutions. x= where k Z #9 Points possible: 1. Total attempts: 3 Give the smallest two solutions of cos(2) = 0.4304 on [ 0, 2 ). Separate the two solutions with a comma. #10 Points possible: 1. Total attempts: 3 Solve 6 cos2 (x) sin(x) 5 = 0 for all solutions 0 x < 2 x= Give your answers accurate to 2 decimal places, as a list separated by commas 1. 2 3 4 \f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\fAssignment 7.5 Solving Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Solve sin(x) = 0.18 on 0 x < 2. There are two solutions, A and B, with A < B. A= B= Give your answers accurate to 3 decimal places. #2 Points possible: 1. Total attempts: 3 Solve 7 cos(5x) = 6 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas. #3 Points possible: 1. Total attempts: 3 Find all solutions to 2 cos() = 1 on the interval 0 < 2. = Give your answers as exact values in a list separated by commas. #4 Points possible: 1. Total attempts: 3 Solve for t, 0 t < 2. 20 sin(t)cos(t) = 12 cos(t) t= Give your answers as values rounded to at least two decimal places in a list separated by commas. #5 Points possible: 1. Total attempts: 3 Solve 4 sin2 (w) 14 sin(w) + 6 = 0 for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #6 Points possible: 1. Total attempts: 3 Solve sin2 (w) = 3 cos(w) for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #7 Points possible: 1. Total attempts: 3 Solve 8 sin(2t) 14 sin(t) = 0 for all solutions 0 t < 2. t= Give your answers accurate to at least 2 decimal places and in a list separated by commas. #8 Points possible: 1. Total attempts: 3 Solve 2 cos2 (x) 7 cos(x) + 5 = 0 for all solutions. x= where k Z #9 Points possible: 1. Total attempts: 3 Give the smallest two solutions of sin(8) = 0.7057 on [ 0, 2 ). Separate the two solutions with a comma. #10 Points possible: 1. Total attempts: 3 Solve 12 sin2 (w) + 10 cos(w) 14 = 0 for all solutions 0 w < 2 w= Give your answers accurate to 2 decimal places, as a list separated by commas \f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\fA population of rabbits oscillates 20 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 800 rabbits and increases by 170 each year. Find an equation for the population, P, in terms of the months since January, t. .P(t) = ' ' Preview Get help: Videol Points possible: 1 License This is attempt 1 of 3. A population of rabbits oscillates 35 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 850 rabbits and increases by 150 each year. Find an equation for the population, P, in terms of the months since January, t. P(t)=_ 1 Answer: 35 - cos(% - t) + (g) -t + 850 \f\f\fFind a possible formula for the trigonometric function whose values are in the following table. Bum-I\" \"III-\"I Hint: Plot the points and sketch your own graph if needed. y=. Answer: 3 - sin(% - (a: 3)) 1 \fHello Pradeep, I know you tried contacting me through skype and sent you a request. The states means I am in the USA. Is it possible for you to consider an alternate method of communication for example whatsapp or your email, that way it will be easy for you to receive uploaded documents quicker for your assistance for the 6 th of july at 0900 pacific standard time and for the work to come?? Also if you would like to consider an alternate payment method that way you can get full compensation instead of receiving half. Please let me know whether this works for you. Assignment 7.5 Solving Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Solve sin(x) = 0.39 on 0 x < 2. There are two solutions, A and B, with A < B. A= B= Give your answers accurate to 3 decimal places. #2 Points possible: 1. Total attempts: 3 Solve 4 cos(3x) = 3 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas. #3 Points possible: 1. Total attempts: 3 Find all solutions to 2 cos() = 3 on the interval 0 < 2. = Give your answers as exact values in a list separated by commas. #4 Points possible: 1. Total attempts: 3 Solve for t, 0 t < 2. 20 sin(t)cos(t) = 12 cos(t) t= Give your answers as values rounded to at least two decimal places in a list separated by commas. #5 Points possible: 1. Total attempts: 3 Solve 2 cos2 (w) 5 cos(w) + 2 = 0 for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #6 Points possible: 1. Total attempts: 3 Solve sin2 (w) = 6 cos(w) for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #7 Points possible: 1. Total attempts: 3 Solve 7 sin(2) + 5 sin() = 0 for all solutions 0 < 2. = Give your answers accurate to at least 2 decimal places and in a list separated by commas. #8 Points possible: 1. Total attempts: 3 Solve 2 cos2 (x) cos(x) 3 = 0 for all solutions. x= where k Z #9 Points possible: 1. Total attempts: 3 Give the smallest two solutions of cos(2) = 0.4304 on [ 0, 2 ). Separate the two solutions with a comma. #10 Points possible: 1. Total attempts: 3 Solve 6 cos2 (x) sin(x) 5 = 0 for all solutions 0 x < 2 x= Give your answers accurate to 2 decimal places, as a list separated by commas 1. 2 3 4 \f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\fAssignment 7.5 Solving Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Solve sin(x) = 0.18 on 0 x < 2. There are two solutions, A and B, with A < B. A= B= Give your answers accurate to 3 decimal places. #2 Points possible: 1. Total attempts: 3 Solve 7 cos(5x) = 6 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas. #3 Points possible: 1. Total attempts: 3 Find all solutions to 2 cos() = 1 on the interval 0 < 2. = Give your answers as exact values in a list separated by commas. #4 Points possible: 1. Total attempts: 3 Solve for t, 0 t < 2. 20 sin(t)cos(t) = 12 cos(t) t= Give your answers as values rounded to at least two decimal places in a list separated by commas. #5 Points possible: 1. Total attempts: 3 Solve 4 sin2 (w) 14 sin(w) + 6 = 0 for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #6 Points possible: 1. Total attempts: 3 Solve sin2 (w) = 3 cos(w) for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #7 Points possible: 1. Total attempts: 3 Solve 8 sin(2t) 14 sin(t) = 0 for all solutions 0 t < 2. t= Give your answers accurate to at least 2 decimal places and in a list separated by commas. #8 Points possible: 1. Total attempts: 3 Solve 2 cos2 (x) 7 cos(x) + 5 = 0 for all solutions. x= where k Z #9 Points possible: 1. Total attempts: 3 Give the smallest two solutions of sin(8) = 0.7057 on [ 0, 2 ). Separate the two solutions with a comma. #10 Points possible: 1. Total attempts: 3 Solve 12 sin2 (w) + 10 cos(w) 14 = 0 for all solutions 0 w < 2 w= Give your answers accurate to 2 decimal places, as a list separated by commas \f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\f\fA population of rabbits oscillates 20 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 800 rabbits and increases by 170 each year. Find an equation for the population, P, in terms of the months since January, t. .P(t) = ' ' Preview Get help: Videol Points possible: 1 License This is attempt 1 of 3. A population of rabbits oscillates 35 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 850 rabbits and increases by 150 each year. Find an equation for the population, P, in terms of the months since January, t. P(t)=_ 1 Answer: 35 - cos(% - t) + (g) -t + 850 \f\f\fFind a possible formula for the trigonometric function whose values are in the following table. Bum-I\" \"III-\"I Hint: Plot the points and sketch your own graph if needed. y=. Answer: 3 - sin(% - (a: 3)) 1 \fHello Pradeep, I know you tried contacting me through skype and sent you a request. The states means I am in the USA. Is it possible for you to consider an alternate method of communication for example whatsapp or your email, that way it will be easy for you to receive uploaded documents quicker for your assistance for the 6 th of july at 0900 pacific standard time and for the work to come?? Also if you would like to consider an alternate payment method that way you can get full compensation instead of receiving half. Please let me know whether this works for you