Ch. 1 - Angles and the Trigonometric Functions
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- In Exercises 5β18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, π, π, π, 2π, 5π, π, 7π, 4π, 3π, 5π, 11π, and 2π. 6 3 2 3 6 6 3 2 3 6 Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
Problem 12
In Exercises 11β18, continue to refer to the figure at the bottom of the previous page. csc 4π/3
- In Exercises 5β12, graph two periods of the given tangent function. y = tan(x β Ο/4)
Problem 12
- Use the figure shown to solve Exercises 13β16. Find the bearing from O to A.
Problem 13
- In Exercises 13β16, the graph of a cotangent function is given. Select the equation for each graph from the following options: y = cot(x + Ο/2), y = cot(x + Ο), y = βcot x, y= βcot(x β Ο/2).
Problem 13
- In Exercises 5β18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, π, π, π, 2π, 5π, π, 7π, 4π, 3π, 5π, 11π, and 2π. 6 3 2 3 6 6 3 2 3 6 Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
Problem 14
In Exercises 11β18, continue to refer to the figure at the bottom of the previous page. sec 5π/3
- In Exercises 5β18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, π, π, π, 2π, 5π, π, 7π, 4π, 3π, 5π, 11π, and 2π. 6 3 2 3 6 6 3 2 3 6 Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
Problem 16
In Exercises 11β18, continue to refer to the figure at the bottom of the previous page. cos 3π/2
- In Exercises 17β24, graph two periods of the given cotangent function. y = 2 cot x
Problem 17
- In Exercises 17β20, ΞΈ is an acute angle and sin ΞΈ and cos ΞΈ are given. Use identities to find tan ΞΈ, csc ΞΈ, sec ΞΈ, and cot ΞΈ. Where necessary, rationalize denominators. sin ΞΈ = 3/5, cos ΞΈ = 4/5
Problem 18
- In Exercises 5β18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, π, π, π, 2π, 5π, π, 7π, 4π, 3π, 5π, 11π, and 2π. 6 3 2 3 6 6 3 2 3 6 Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
Problem 18
In Exercises 11β18, continue to refer to the figure at the bottom of the previous page. tan 3π/2
- In Exercises 19β24, a. Use the unit circle shown for Exercises 5β18 to find the value of the trigonometric function. b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number. cos (-π/6)
Problem 19
- In Exercises 17β24, graph two periods of the given cotangent function. y = 1/2 cot 2x
Problem 19
- In Exercises 18β24, graph two full periods of the given tangent or cotangent function. y = β2 tan Ο/4 x
Problem 19
- In Exercises 17β20, ΞΈ is an acute angle and sin ΞΈ and cos ΞΈ are given. Use identities to find tan ΞΈ, csc ΞΈ, sec ΞΈ, and cot ΞΈ. Where necessary, rationalize denominators. __ sin ΞΈ = 6, cos ΞΈ = β13 7 7
Problem 20
- In Exercises 19β24, a. Use the unit circle shown for Exercises 5β18 to find the value of the trigonometric function. b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number. cos π/3
Problem 20
- In Exercises 21β24, ΞΈ is an acute angle and sin ΞΈ is given. Use the Pythagorean identity sinΒ²ΞΈ + cosΒ²ΞΈ = 1 to find cos ΞΈ. sin ΞΈ = 6/7
Problem 21
- In Exercises 19β24, a. Use the unit circle shown for Exercises 5β18 to find the value of the trigonometric function. b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number. sin 5π/6
Problem 21
- In Exercises 17β24, graph two periods of the given cotangent function. y = β3 cot Ο/2 x
Problem 21
- In Exercises 18β24, graph two full periods of the given tangent or cotangent function. y = βtan(x β Ο/4)
Problem 21
- In Exercises 21β28, 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 = 10 cos 2Οt
Problem 22
- In Exercises 21β24, ΞΈ is an acute angle and sin ΞΈ is given. Use the Pythagorean identity sinΒ²ΞΈ + cosΒ²ΞΈ = 1 to find cos ΞΈ. __ sin ΞΈ = β39 8
Problem 23
- In Exercises 19β24, a. Use the unit circle shown for Exercises 5β18 to find the value of the trigonometric function. b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number. tan 5π/3
Problem 23
- In Exercises 17β24, graph two periods of the given cotangent function. y = 3 cot(x + Ο/2)
Problem 23
- In Exercises 18β24, graph two full periods of the given tangent or cotangent function. y = β 1/2 cot Ο/2 x
Problem 23
- In Exercises 19β24, a. Use the unit circle shown for Exercises 5β18 to find the value of the trigonometric function. b. Use even and odd properties of trigonometric functions and your answer from part (a) to find the value of the same trigonometric function at the indicated real number. tan (-11π/6)
Problem 24
- In Exercises 21β28, 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 = β8 cos Ο/2 t
Problem 24
- In Exercises 25β30, use an identity to find the value of each expression. Do not use a calculator. sin 37Β° csc 37Β°
Problem 25
- In Exercises 25β32, the unit circle has been divided into eight equal arcs, corresponding to t-values of 0, π, π, 3π, π, 5π, 3π, 7π, and 2π. 4 2 4 4 2 4 a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function. b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.
Problem 25
sin 11π/4
- In Exercises 21β28, 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 = 1/3 sin 2t
Problem 26
Problem 26a
In Exercises 25β32, the unit circle has been divided into eight equal arcs, corresponding to t-values of
0, π, π, 3π, π, 5π, 3π, 7π, and 2π.
4 2 4 4 2 4
a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.
cos 3π/4
- In Exercises 25β32, the unit circle has been divided into eight equal arcs, corresponding to t-values of 0, π, π, 3π, π, 5π, 3π, 7π, and 2π. 4 2 4 4 2 4 a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function. b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.
Problem 27
cos 9π/2