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study help
mathematics
precalculus
Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions
In Problems 11 – 26, use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator. tan (217)
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = -2 sin(-4x - 2π) - 2
In Problems 21 – 30, find the exact value. Do not use a calculator. cos (7π)
In Problems 15–24, determine the amplitude and period of each function without graphing. y = sin 3 2 3
In Problems 31 – 46, find the exact value of each expression. Do not use a calculator.sin45° + cos60°
In Problems 17–40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. cot (1 4 y = cot ·X
In Problems 11 – 26, use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator. 9T csc- 2 |
In Problems 16–23, find the exact value of each of the remaining trigonometric functions. sec 0 - 3, Зп 2
In Problems 15–24, determine the amplitude and period of each function without graphing. y: 10 2 마렇지 5 -sin
In Problems 16–23, find the exact value of each of the remaining trigonometric functions. cote = -2, π 2 < 0 < T
In Problems 15–24, determine the amplitude and period of each function without graphing. y = 7 (x 1 - = soo. 6
In Problems 11 – 26, use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator. 17T 4 sec.
In Problems 17–40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y = cot (x)
In Problems 11 – 26, use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator. 17T 4 cot-
In Problems 5–15, find the exact value of each expression. Do not use a calculator. sin 310° csc (-50°)
In Problems 13 – 20, P = (x, y) is the point on the unit circle that corresponds to a real number t. Find the exact values of the six trigonometric functions of t. 2√6 5' 5 1 -lin
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = 2 tan(4x - π)
In Problems 13–16, use a calculator to evaluate each expression. Round your answer to three decimal places. 28T 9 cot:
In Problems 16–23, find the exact value of each of the remaining trigonometric functions. sin0 = 4 5' 0 is acute
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = 1/cot (2x - - π)
In Problems 15–24, determine the amplitude and period of each function without graphing.y = 5 sin x
In Problems 16–23, find the exact value of each of the remaining trigonometric functions. tane 12 5 sin < 0 0
In Problems 11–22, draw each angle in standard position.450°
In Problems 16–23, find the exact value of each of the remaining trigonometric functions.$#!#$ sec 0 = 5 nit 4 tane < 0
In Problems 16–23, find the exact value of each of the remaining trigonometric functions. sin 12 13' 0 in quadrant II
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = 3 csc (2x - 7) 4
In Problems 11 – 26, use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator. cos 33п 4
In Problems 15–24, determine the amplitude and period of each function without graphing.y = −3 cos(4x)
In Problems 11 – 26, use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.cot 390°
In Problems 15–24, determine the amplitude and period of each function without graphing. y = -3 cos (3x)
If f (x) = sin x and f (a)= 3/5, find f (−a).
In Problems 13–16, use a calculator to evaluate each expression. Round your answer to three decimal places. sec 229°
In Problems 13 – 20, P = (x, y) is the point on the unit circle that corresponds to a real number t. Find the exact values of the six trigonometric functions of t. √√21 5' 5
In Problems 5–15, find the exact value of each expression. Do not use a calculator. sin (-40°) sin 40°
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = = 2 sin (2πx 4) - 1
In Problems 13–16, use a calculator to evaluate each expression. Round your answer to three decimal places. cos 27T 5
In Problems 5–15, find the exact value of each expression. Do not use a calculator. cos (-40°) cos 40°
In Problems 13 – 20, P = (x, y) is the point on the unit circle that corresponds to a real number t. Find the exact values of the six trigonometric functions of t. HIN √3 2
g(x) = cos x(a) What is the y-intercept of the graph of g?(b) For what numbers x, −π ≤ x ≤ π, is the graph of g decreasing?(c) What is the absolute minimum of g?(d) For what numbers x, 0 ≤ x ≤ 2π, does g(x) = 0?(e) For what numbers x, −2π ≤ x ≤ 2π, does g(x) = 1? Where does
f(x) = sin x(a) What is the y-intercept of the graph of f?(b) For what numbers x, −π ≤ x ≤ π, is the graph of f increasing?(c) What is the absolute maximum of f?(d) For what numbers x, 0 ≤ x ≤ 2π, does f (x) = 0?(e) For what numbers x, −2π ≤ x ≤ 2π, does f (x) = 1? Where does f
In Problems 11–22, draw each angle in standard position.135°
In Problems 11 – 26, use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator.tan405°
In Problems 13–16, use a calculator to evaluate each expression. Round your answer to three decimal places. sin 17⁰
The point on the unit circle that corresponds to θ = π/3 is (a) (c) 123_2 √√3 22 (b) 识别 2√3 (d) 15, 255) 3
In Problems 5–15, find the exact value of each expression. Do not use a calculator. sec 50°cos 50°
To graph y = 3 sin(−2x) using key points, the equivalent form_____ could be graphed instead.(a) y = −3 sin(−2x)(b) y = −2 sin(3x)(c) y = 3 sin(2x)(d) y = −3 sin(2x)
In Problems 7–12, find the exact value of each expression. 2 sin ² 60° - 3 cos 45°
In Problems 7–12, find the exact value of each expression. KIN sin- 19T 4 - tan-
In Problems 5–15, find the exact value of each expression. Do not use a calculator. sin² 20° + 1 sec2 20°
In Problems 11–22, draw each angle in standard position.60°
One period of the graph of y = sin (ωx) or y = cos(ωx) is called a(n).(a) Amplitude(b) Phase shift(c) Transformation(d) Cycle
Find the exact value of tan/4 −3 cosπ/6 +cscπ/6.
In Problems 5–15, find the exact value of each expression. Do not use a calculator. cos540° tan(-405°)
The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Sunday, March 27, 2022, in Charleston, South Carolina, high tide occurred at 1:10 am (1.2 hours) and low tide occurred at 7:44 am (7.73 hours). Water
In Problems 17–40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. y = tan tan(x). +1
In Problems 27 – 34, name the quadrant in which the angle θ lies. sec 0 0, sin > 0
(a) Check the box “Show Unit Circle.” Be sure the “Show Graph” and “Show Key Points” boxes are unchecked. Use your cursor to slowly move the point on the “Drag me!” slider. Notice the point in blue on the unit circle moves in a counter-clockwise direction. Also, notice the points in
(a) Check the box “Show Unit Circle.” Be sure the “Show Graph” and “Show Key Points” boxes are unchecked. Use your cursor to slowly move the point on the “Drag me!” slider. Notice the point in blue on the unit circle moves in a counter-clockwise direction. Also, notice the points in
In Problems 3 and 4, convert each angle in radians to degrees. Зп 4
True or False The function f (x) = √x is even.
In Problems 3 and 4, convert each angle in radians to degrees. 5п 2
In Problems 4–6, convert each angle in radians to degrees. π 8
The equation x2 + 2x = (x + 1)2 − 1 is an identity.
In Problems 4–6, convert each angle in radians to degrees. Зп 4
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = 3 cos(2x + π)
In Problems 5–15, find the exact value of each expression. Do not use a calculator. π 3 sin 45° 4 tan. - 6
Which of the following is not in the range of the sine function? (a) (b) N/W (c) -0.37 (d) -1
In Problems 7–12, find the exact value of each expression. sin 7 6
The domain of the tangent function is _____.
Answers are given at the end of these exercises.180° = radians (a) 플 (b) a 아 Зп 2 (d) 2
In Problems 5–15, find the exact value of each expression. Do not use a calculator. 3π 4 6 cos- (-5) 3. + 2 tan
In Problems 7–12, find the exact value of each expression. cos(-57) - 4 3π 4 cos-
In Problems 5–15, find the exact value of each expression. Do not use a calculator. sec(-) - cot(-57) 4
Which of the following functions is even?(a) Cosine(b) Sine(c) Tangent(d) Cosecant
In Problems 7–12, find the exact value of each expression. cos(-120°)
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = 4 cos(4x + π) - 2
True or False The graphs of y = sin x and y = cos x are identical except for a horizontal shift.
In Problems 5–15, find the exact value of each expression. Do not use a calculator. tan + sin T
In Problems 7–12, find the exact value of each expression. tan 330°
Find the exact value of (sin14°)2 + (cos14°)2 − 3.
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = 5 sin(4x + π) + 3
True or False sec 0 = 1 sin 0
Answers are given at the end of these exercises.sin2θ+ cos2θ= ____
True or False For y = 2 sin(πx), the amplitude is 2 and the period is π/2.
In Problems 5–15, find the exact value of each expression. Do not use a calculator. π tan 4 π sin- 6
It is easiest to graph y = sec x by first sketching the graph of _______.(a) y = sin x(b) y = cos x(c) y = tan x(d) y = csc x
The maximum value of y = sin x, 0 ≤ x ≤ 2π, is___ and occurs at x = _____.
In Problems 3 – 22, find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. y = 2 = 2 cos (3x + 1)
In Problems 4–6, convert each angle in radians to degrees. 9п 2
The domain of the function f(x) = x+1 - is 2x + 1
Use transformations to graph y = 3x2.
In Problems 1–3, convert each angle in degrees to radians. Express your answer as a multiple of π.−400°
True or False A graphing utility requires only two data points to find the sine function of best fit.
True or False If x = 3 is a vertical asymptote of the graph of a rational function R , then as x → 3,|R(x) →∞.
Answers are given at the end of these exercises.(a) Check the box “Show Unit Circle.” Be sure the “Show Graph,” “Show Key Points,” and “Show Asymptotes” boxes are unchecked. Use your cursor to slowly move the point on the “Drag me!” slider to the right. Notice the point on the
In Problems 1 and 2, convert each angle in degrees to radians. Express your answer as a multiple of π.18°
The value of the function f (x) = 3x − 7 at 5 is _____.
Find the real solutions, if any, of the equation 2x2 + x − 1 = 0
(a) Use the drop-down menu to select the absolute value (x) function. The basic function f (x) =|x| is drawn in a dashed-blue line with three key points labeled. Now, use the slider labeled k to slowly increase the value of k from 0 to 3. As you do this, notice the form of the function g(x) = f (x
(a) In the interactive figure, a represents the exponent on the factor x − 1 in the denominator, while b represents the exponent on the factor x + 2 in the denominator. What are the equations of the two vertical asymptotes on the graph of R?(b) Use the slider to change the value of a to 1 and the
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