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mathematics
precalculus 1st
Precalculus 1st Edition Jay Abramson - Solutions
For the following exercises, determine the amplitude, period, and midline of the graph, and then find a formula for the function.Give in terms of a sine function. -3 -21 y A A -6- + 3
For the following exercises, graph two full periods. Identify the period, the phase shift, the amplitude, and asymptotes.f(x) = 4csc(5x)
For the following exercises, find the period and horizontal shift of each of the functions.If csc x = −5, find csc(−x).
For the following exercises, determine the amplitude, period, and midline of the graph, and then find a formula for the function.Give in terms of a sine function. y 64 2+ -2 NA -4 2 نیا X
For the following exercises, evaluate the expressions.tan−1(√3)
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.y = 3sin(8(x + 4)) + 5
For the following exercises, graph two full periods. Identify the period, the phase shift, the amplitude, and asymptotes.f(x) = 3cot x
For the following exercises, find the period and horizontal shift of each of the functions.If sec x = 2, find sec(−x).
For the following exercises, evaluate the expressions.tan−1(−1)
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline. f(x) = 2csc (x + 1) - 4 3
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = 3cos (6/5 x)
For the following exercises, graph two full periods. Identify the period, the phase shift, the amplitude, and asymptotes. f(x) = 1/3 sec x
For the following exercises, find the period and horizontal shift of each of the functions.If tan x = −1.5, find tan(−x).
For the following exercises, find the period and horizontal shift of each of the functions. m(x) = 6csc
For the following exercises, evaluate the expressions.tan−1 (−√3)
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = 4cos(πx)
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. f(x) = 0.2cos(0.1x) + 0.3
For the following exercises, evaluate the expressions.tan−1(1)
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = 2sin (1/2 x)
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = πsec (π/2 x)
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = −3tan(4x) − 2
For the following exercises, find the period and horizontal shift of each of the functions. h(x) = 2sec ( 7 (x + 1))
For the following exercises, evaluate the expressions. cos V2 2
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = cos(2x)
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = 5csc(3x)
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = 2tan(x − π/6)
For the following exercises, evaluate the expressions. COS 2
For the following exercises, find the period and horizontal shift of each of the functions.f(x) = 2tan(4x − 32)
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = 2cos x
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = πcos(3x + π)
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = tan x − 4
For the following exercises, match each trigonometric function with one of the graphs in Figure 18.f(x) = cot x -2π -I II x = π 277 x Figure 18 5 III -2π A IV x
For the following exercises, evaluate the expressions. sin-( 2
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = 4sin x
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline. f(x) = -2tan (x-7)+2
For the following exercises, match each trigonometric function with one of the graphs in Figure 18.f(x) = csc x 플 EIN +5/0 -2π -A II x = π 27 x Figure 18 EIN y + -RIN III -2π -T y IV 77 2π
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = −100sin(50x − 20)
For the following exercises, evaluate the expressions. sin V2 2
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = −3sin x
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = tan(4x)
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. f(x) = 6sin (3x in (3x 6 - 1
For the following exercises, match each trigonometric function with one of the graphs in Figure 18.f(x) = sec x ਨੂੰ y 플 n +++ -21 II ★ = 2 x Figure 18 [ ਨੂੰ III E x T - IV c ► X 21
Determine whether the following statement is true or false and explain your answer: arccos(−x) = π − arccos x.
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = 2/3 cos x
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. f(x)=2(cos(x-4)+1)
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = 3cos (1/3 x−5π/6)
For the following exercises, match each trigonometric function with one of the graphs in Figure 18.f(x) = tan x II X = N 21 Figure 18 III -21 IV Activate l
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline. f(x) = 5sin (3(x- 77)) + 4 6
Discuss why this statement is incorrect: arccos (cos x) = x for all x.
For the following exercises, graph two full periods of each function and state the amplitude, period, and midline. State the maximum and minimum y-values and their corresponding x-values on one period for x > 0. Round answers to two decimal places if necessary.f(x) = 2sin x
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. f(x) = 3sin(x -- ¹(x-7). - 4 4
How does the period of y = csc x compare with the period of y = sin x?
Why must the domain of the sine function, sin x, be restricted to [− π/2 , π/2] for the inverse sine function to exist?
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = −cos (x + π/3) +1
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes. f(x) = -2sin(x 2π 3
How can the unit circle be used to construct the graph of f(t) = sin t?
Why are there no intercepts on the graph of y = csc x?
Most calculators do not have a key to evaluate sec−1 (2). Explain how this can be done using the cosine function or the inverse cosine function.
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = sin(3x)
How does the range of a translated sine function relate to the equation y = Asin(Bx + C) + D?
For the equation Acos(Bx + C) + D, what constants affect the range of the function and how do they affect the range?
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = 3cos (x + π/6)
Explain how the graph of the sine function can be used to graph y = csc x.
For the following exercises, use identities to simplify the expression.csc t tan t
A wheel on a tractor has a 24-inch diameter. How many revolutions does the wheel make if the tractor travels 4 miles?
Explain why the period of tan x is equal to π.
Explain the meaning of π/6 = arcsin(0.5).
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = 5sin x
How does the graph of y = sin x compare with the graph of y = cos x? Explain how you could horizontally translate the graph of y = sin x to obtain y = cos x.
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = 1/4 sin x
How can the graph of y = cos x be used to construct the graph of y = sec x?
Since the functions y = cos x and y = cos−1 x are inverse functions, why is cos−1 (cos (− π/6)) not equal to −π/6 ?
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = 5cos x
Why are the sine and cosine functions called periodic functions?
For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.f(x) = −3cos x + 3
Why do the functions f(x) = sin−1 x and g(x) = cos−1 x have different ranges?
For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline.f(x) = 0.5sin x
For the following exercises, use this scenario: A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counter clockwise.When will the child have coordinates (−0.866,−0.5) if
For the following exercises, use this scenario: A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counter clockwise.When will the child have coordinates (0.707,–0.707) if
For the following exercises, use this scenario: A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counter clockwise.What is the coordinates of the child after 125 seconds?
For the following exercises, use this scenario: A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counter clockwise.What are the coordinates of the child after 90 seconds?
For the following exercises, use this scenario: A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counter clockwise.What are the coordinates of the child after 45 seconds?
For the following exercises, use a graphing calculator to evaluate. sin(7) sin( TT 6
For the following exercises, use a graphing calculator to evaluate. sin -5T 4 in( sin 117 6
For the following exercises, use a graphing calculator to evaluate. s(37) cos (4) COS COS
For the following exercises, use a graphing calculator to evaluate. 5π s ( 57 ) cos ( 31 ) 6 COS
For the following exercises, use a graphing calculator to evaluate. sin (7) cos (37) COS 6
For the following exercises, use a graphing calculator to evaluate. sin 7π (77) cos(-37) COS 4
For the following exercises, use a graphing calculator to evaluate. sin I) cos(= -91 4 一π 6
For the following exercises, use a graphing calculator to evaluate. sin I) cos(= -91 4 一π 6
For the following exercises, use a graphing calculator to evaluate. sin Зл (37) cos (57 3
For the following exercises, use a graphing calculator to evaluate. sin 11π 5п (117) Co (-5π) cos 3 6
For the following exercises, use a graphing calculator to evaluate.sin 310°
For the following exercises, use a graphing calculator to evaluate.cos 310°
For the following exercises, use a graphing calculator to evaluate.cos 98°
For the following exercises, use a graphing calculator to evaluate.sin 98°
For the following exercises, use a graphing calculator to evaluate.cos 3π/4
For the following exercises, use a graphing calculator to evaluate.sin 3π/4
For the following exercises, use the given point on the unit circle to find the value of the sine and cosine of t. (0, 1) t
For the following exercises, use a graphing calculator to evaluate.cos π/10
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