In Exercises 21–28, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, find the following: a. the maximum displacement b. the frequency c. the time required for one cycle. d = −4 sin 3π/2 t

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 37–40, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, graph one period of the equation. Then find the following: a. the maximum displacement b. the frequency c. the time required for one cycle d. the phase shift of the motion. d = 3 cos(πt + π/2)

In Exercises 37–40, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in inches. In each exercise, graph one period of the equation. Then find the following: a. the maximum displacement b. the frequency c. the time required for one cycle d. the phase shift of the motion. d = − 1/2 sin(πt/4 − π/2)

Determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin 4x

Determine the amplitude and period of each function. Then graph one period of the function. y = (1/2) sin (π/3) x

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 cos (x + π)

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 sin(π/3 x − 3π)

In Exercises 12–13, use a vertical shift to graph one period of the function. y = 2 cos 1/3 x − 2

In Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = sin x + cos 1/2 x

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = −2 tan π/4 x

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = −tan(x − π/4)

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = − 1/2 cot π/2 x

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ sin⁻¹ (− √3/2)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. cos⁻¹ (− 1/2)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sec⁻¹ (−1)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ cos(sin⁻¹ √2/2)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. tan[sin⁻¹ (− 1/2)]

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ csc(tan⁻¹ √3/3)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin(cos⁻¹ 3/5)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. tan [cos⁻¹ (− 4/5)]

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin⁻¹(sin π/3)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin⁻¹(cos 2π/3)

In Exercises 52–53, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sec(sin⁻¹ 1/x)

In Exercises 54–57, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. A = 22.3°, c = 10

In Exercises 61–62, use the figures shown to find the bearing from O to A.

In Exercises 65–66, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in centimeters. In each exercise, find: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 20 cos π/4 t