5.1 Angles Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Convert the angle 224 to radians. Give the exact value. This means there should be a in your answer. 56/45 pi #2 Points possible: 1. Total attempts: 3 Convert the angle 140 7 radians to degrees. 9 degrees #3 Points possible: 1. Total attempts: 3 An angle in standard position measures 1025 . The coterminal angle with measure between 0 and 360 has measure 305 degrees. #4 Points possible: 1. Total attempts: 3 Are the standard position angles measuring 17 and 377 coterminal? Your answer (input yes or no) is : yes . #5 Points possible: 1. Total attempts: 3 The angle between 0 and 360 that is coterminal with the 549 angle is degrees -189 #6 Points possible: 1. Total attempts: 3 The angle between 0 and 2 in radians that is coterminal with the angle . 44 radians is 9 #7 Points possible: 1. Total attempts: 3 On a circle of radius 8 feet, what angle would subtend an arc of length 2 feet? degrees #8 Points possible: 1. Total attempts: 3 Find the area of the sector formed by the angle 210 with a radius of 7.6. Give your answer rounded to 2 decimal places. #9 Points possible: 1. Total attempts: 3 A truck with 38-in.-diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min: rad/min How many revolutions per minute do the wheels make? #10 Points possible: 1. Total attempts: 3 On a circle of radius 8 feet, what angle would subtend an arc of length 3 feet? radians rpm Assignment 5.2 Unit Circle: Sine and Cosine Functions Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 From the information given, find the quadrant in which the terminal point determined by t lies. Input I, II, III, or IV. (a) sin(t) < 0 and cos(t) < 0, quadrant ; (b) sin(t) > 0 and cos(t) < 0, quadrant ; (c) sin(t) > 0 and cos(t) > 0, quadrant ; (d) sin(t) < 0 and cos(t) > 0, quadrant ; #2 Points possible: 1. Total attempts: 3 Find an angle with 0 < < 360 that has the same: Sine function value as 220 = degrees Cosine function value as 220 = degrees #3 Points possible: 1. Total attempts: 3 If cos() = 1 and is in the 4th quadrant, find the exact value for sin(). 9 sin() = #4 Points possible: 1. Total attempts: 3 Without using a calculator, compute the sine and cosine of 135 by using the reference angle. What is the reference angle? In what quadrant is this angle? sin(135 ) = cos(135 ) = (Type sqrt(2) for 2 and sqrt(3) for 3.) degrees. (answer 1, 2, 3, or 4) #5 Points possible: 1. Total attempts: 3 Without using a calculator, compute the sine and cosine of 5 by using the reference angle. 4 What is the reference angle? radians. In what quadrant is this angle? (answer 1, 2, 3, or 4) sin( 5 )= 4 cos( 5 )= 4 (Type sqrt(2) for 2 and sqrt(3) for 3.) #6 Points possible: 1. Total attempts: 3 If = 1 , then 4 sin() = cos() = Give exact values. No decimals allowed! #7 Points possible: 1. Total attempts: 3 If = 4 , then 3 sin() = cos() = Give exact values. No decimals allowed! #8 Points possible: 1. Total attempts: 3 If = 7 , then 6 sin() = cos() = Give exact values. No decimals allowed! 2 . With functions like sqrt, be sure to use function notation 2 (parentheses). sqrt(2)/2 will work, but sqrt2/2 will not. Example: Enter sqrt(2)/2 for #9 Points possible: 1. Total attempts: 3 Find the coordinates of a point on a circle with radius 15 corresponding to an angle of 330 (x,y) = ( , ) Round your answers to three decimal places. #10 Points possible: 1. Total attempts: 3 Find an angle with 0 < < 360 that has the same: Sine as 50 : = Cosine as 50 : = degrees degrees Assignment 5.3 The Other Trigonometric Functions #1 Points possible: 1. Total attempts: 3 If = 7 , then find exact values for the following: 4 sec() equals csc() equals tan() equals cot() equals #2 Points possible: 1. Total attempts: 3 If = 5 , then find exact values for the following: 6 sec() equals csc() equals tan() equals cot() equals #3 Points possible: 1. Total attempts: 3 If sin() = (a) cos() = (b) tan() = (c) sec() = (d) csc() = (e) cot() = 3 , and is in quadrant III , then find 8 Name: Syd Hendricks #4 Points possible: 1. Total attempts: 3 If tan() = 24 , 0 , then 7 2 sin() equals cos() equals sec() equals #5 Points possible: 1. Total attempts: 3 Given that the point (160, -36) is on the terminal side of an angle, , find the exact value of the following: sin()= cos()= tan()= csc()= sec()= cot()= #6 Points possible: 1. Total attempts: 3 Find the terminal point P (x, y) on the unit circle determined by the given angle in degrees: (a) 90 degrees, then x = and y = ; (b) -90 degrees, then x = and y = ; (c) 60 degrees, then x = and y = ; (d) -60 degrees, then x = and y = ; (e) 135 degrees, then x = and y = ; (f) -135 degrees, then x = and y = ; #7 Points possible: 1. Total attempts: 3 (a) If t = 0 degrees, sin(t) = (b) If t = 45 degrees, sin(t) = (c) If t = 90 degrees, sin(t) = (d) If t = 135 degrees, sin(t) = (e) If t = 180 degrees, sin(t) = (f) If t = 225 degrees, sin(t) = (g) If t = 270 degrees, sin(t) = (h) If t = 315 degrees, sin(t) = and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; #8 Points possible: 1. Total attempts: 3 Find an angle with 0 < < 360 that has the same: Sine function value as 240 = degrees Cosine function value as 240 = degrees #9 Points possible: 1. Total attempts: 3 2 and tan < 0, then 4 sin() = ; tan() = ; cot() = ; sec() = ; csc() = ; Give exact values. If cos = #10 Points possible: 1. Total attempts: 3 Find the exact value. tan(1470 ) = cot(1470 ) = ; ; Assignment 5.4 Right Triangle Trigonometry #1 Points possible: 1. Total attempts: 3 Note: Triangle may not be drawn to scale. Suppose a = 12 and b = 7. Find an exact value or give at least two decimal places: sin(A) = cos(A) = tan(A) = sec(A) = csc(A) = cot(A) = Name: Syd Hendricks #2 Points possible: 1. Total attempts: 3 Note: Triangle may not be drawn to scale. Suppose a = 3 and A = 65 degrees. Find: b= c= B= degrees Give all answers to at least one decimal place. Give angles in degrees #3 Points possible: 1. Total attempts: 3 Note: Triangle may not be drawn to scale. Suppose c = 7 and A = 50 degrees. Find: a= b= B= degrees Give all answers to at least one decimal place. Give angles in degrees #4 Points possible: 1. Total attempts: 3 For the right triangle below, find the length of x. Round to the hundredths. (2 decimal places) 8 <-- 45 x #5 Points possible: 1. Total attempts: 3 For the right triangle below, find the length of x. Round to the hundredths. (2 decimal places) <-- 24 12 x #6 Points possible: 1. Total attempts: 3 For the right triangle below, find the measure of the angle. Round to the hundredths. (2 decimal places) <-- ? 13 8 degrees #7 Points possible: 1. Total attempts: 3 A 26-ft ladder leans against a building so that the angle between the ground and the ladder is 82 . How high does the ladder reach on the building? ft #8 Points possible: 1. Total attempts: 3 A radio tower is located 275 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 32 and that the angle of depression to the bottom of the tower is 20 . How tall is the tower? feet #9 Points possible: 1. Total attempts: 3 Find x correct to 2 decimal places. NOTE: The triangle is NOT drawn to scale. 116 47 38 x x= #10 Points possible: 1. Total attempts: 3 The proper angle for a ladder is about 75 degrees from the ground. Suppose you have a 29 foot ladder. How far from the house should you place the base of the ladder? Round to the hundredths. (2 decimal places) feet Chapter 5 Review Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Convert the angle 384 to radians. Give the exact value. This means there should be a in your answer. #2 Points possible: 1. Total attempts: 3 Convert the angle 14 radians to degrees. 15 degrees #3 Points possible: 1. Total attempts: 3 An angle in standard position measures 636 . The coterminal angle with measure between 0 and 360 has measure degrees. #4 Points possible: 1. Total attempts: 3 Are the standard position angles measuring 319 and 679 coterminal? Your answer (input yes or no) is : . #5 Points possible: 1. Total attempts: 3 The angle between 0 and 360 that is coterminal with the 1812 angle is degrees #6 Points possible: 1. Total attempts: 3 The angle between 0 and 2 in radians that is coterminal with the angle . 49 radians is 10 #7 Points possible: 1. Total attempts: 3 On a circle of radius 9 feet, what angle would subtend an arc of length 3 feet? degrees #8 Points possible: 1. Total attempts: 3 Find the area of the sector formed by the angle 600 with a radius of 12.8. Give your answer rounded to 2 decimal places. #9 Points possible: 1. Total attempts: 3 A truck with 46-in.-diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min: rad/min How many revolutions per minute do the wheels make? rpm #10 Points possible: 1. Total attempts: 3 On a circle of radius 5 feet, what angle would subtend an arc of length 7 feet? radians #11 Points possible: 1. Total attempts: 3 From the information given, find the quadrant in which the terminal point determined by t lies. Input I, II, III, or IV. (a) sin(t) < 0 and cos(t) < 0, quadrant ; (b) sin(t) > 0 and cos(t) < 0, quadrant ; (c) sin(t) > 0 and cos(t) > 0, quadrant ; (d) sin(t) < 0 and cos(t) > 0, quadrant ; #12 Points possible: 1. Total attempts: 3 Find an angle with 0 < < 360 that has the same: Sine function value as 230 = degrees Cosine function value as 230 = degrees #13 Points possible: 1. Total attempts: 3 If cos() = sin() = 3 and is in the 1st quadrant, find the exact value for sin(). 5 #14 Points possible: 1. Total attempts: 3 Without using a calculator, compute the sine and cosine of 120 by using the reference angle. What is the reference angle? In what quadrant is this angle? degrees. (answer 1, 2, 3, or 4) sin(120 ) = cos(120 ) = (Type sqrt(2) for 2 and sqrt(3) for 3.) #15 Points possible: 1. Total attempts: 3 Without using a calculator, compute the sine and cosine of 4 by using the reference angle. 3 What is the reference angle? radians. In what quadrant is this angle? (answer 1, 2, 3, or 4) sin( 4 )= 3 cos( 4 )= 3 (Type sqrt(2) for 2 and sqrt(3) for 3.) #16 Points possible: 1. Total attempts: 3 If = 3 , then 4 sin() = cos() = Give exact values. No decimals allowed! #17 Points possible: 1. Total attempts: 3 If = 2 , then 3 sin() = cos() = Give exact values. No decimals allowed! #18 Points possible: 1. Total attempts: 3 If = 11 , then 6 sin() = cos() = Give exact values. No decimals allowed! 2 . With functions like sqrt, be sure to use function notation 2 (parentheses). sqrt(2)/2 will work, but sqrt2/2 will not. Example: Enter sqrt(2)/2 for #19 Points possible: 1. Total attempts: 3 Find the coordinates of a point on a circle with radius 5 corresponding to an angle of 140 (x,y) = ( , ) Round your answers to three decimal places. #20 Points possible: 1. Total attempts: 3 Find an angle with 0 < < 360 that has the same: Sine as 70 : = Cosine as 70 : = degrees degrees #21 Points possible: 1. Total attempts: 3 If = 1 , then find exact values for the following: 4 sec() equals csc() equals tan() equals cot() equals #22 Points possible: 1. Total attempts: 3 If = 5 , then find exact values for the following: 6 sec() equals csc() equals tan() equals cot() equals #23 Points possible: 1. Total attempts: 3 If sin() = (a) cos() = (b) tan() = (c) sec() = (d) csc() = (e) cot() = 4 , and is in quadrant III , then find 5 #24 Points possible: 1. Total attempts: 3 If tan() = 4 , 0 , then 3 2 sin() equals cos() equals sec() equals #25 Points possible: 1. Total attempts: 3 Given that the point (-160, 36) is on the terminal side of an angle, , find the exact value of the following: sin()= cos()= tan()= csc()= sec()= cot()= #26 Points possible: 1. Total attempts: 3 Find the terminal point P (x, y) on the unit circle determined by the given angle in degrees: (a) 90 degrees, then x = and y = ; (b) -90 degrees, then x = and y = ; (c) 60 degrees, then x = and y = ; (d) -60 degrees, then x = and y = ; (e) 135 degrees, then x = and y = ; (f) -135 degrees, then x = and y = ; #27 Points possible: 1. Total attempts: 3 (a) If t = 0 degrees, sin(t) = (b) If t = 45 degrees, sin(t) = (c) If t = 90 degrees, sin(t) = (d) If t = 135 degrees, sin(t) = (e) If t = 180 degrees, sin(t) = (f) If t = 225 degrees, sin(t) = (g) If t = 270 degrees, sin(t) = (h) If t = 315 degrees, sin(t) = and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; and cos(t) = ; #28 Points possible: 1. Total attempts: 3 Find an angle with 0 < < 360 that has the same: Sine function value as 260 = degrees Cosine function value as 260 = degrees #29 Points possible: 1. Total attempts: 3 2 and tan < 0, then 3 sin() = ; tan() = ; cot() = ; sec() = ; csc() = ; Give exact values. If cos = #30 Points possible: 1. Total attempts: 3 Find the exact value. tan(1470 ) = cot(1470 ) = ; ; #31 Points possible: 1. Total attempts: 3 Note: Triangle may not be drawn to scale. Suppose a = 2 and b = 12. Find an exact value or give at least two decimal places: sin(A) = cos(A) = tan(A) = sec(A) = csc(A) = cot(A) = #32 Points possible: 1. Total attempts: 3 Note: Triangle may not be drawn to scale. Suppose a = 6 and A = 60 degrees. Find: b= c= B= degrees Give all answers to at least one decimal place. Give angles in degrees #33 Points possible: 1. Total attempts: 3 Note: Triangle may not be drawn to scale. Suppose c = 13 and A = 25 degrees. Find: a= b= B= degrees Give all answers to at least one decimal place. Give angles in degrees #34 Points possible: 1. Total attempts: 3 For the right triangle below, find the length of x. Round to the hundredths. (2 decimal places) 15 <-- 42 x #35 Points possible: 1. Total attempts: 3 For the right triangle below, find the length of x. Round to the hundredths. (2 decimal places) <-- 30 14 x #36 Points possible: 1. Total attempts: 3 For the right triangle below, find the measure of the angle. Round to the hundredths. (2 decimal places) <-- ? 13 7 degrees #37 Points possible: 1. Total attempts: 3 A 35-ft ladder leans against a building so that the angle between the ground and the ladder is 76 . How high does the ladder reach on the building? ft #38 Points possible: 1. Total attempts: 3 A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 30 and that the angle of depression to the bottom of the tower is 22 . How tall is the tower? feet #39 Points possible: 1. Total attempts: 3 Find x correct to 2 decimal places. NOTE: The triangle is NOT drawn to scale. 110 37 40 x x= #40 Points possible: 1. Total attempts: 3 The proper angle for a ladder is about 75 degrees from the ground. Suppose you have a 22 foot ladder. How far from the house should you place the base of the ladder? Round to the hundredths. (2 decimal places) feet