3. Unit Circle

Trigonometric Functions on the Unit Circle

Textbook Question
In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.6 3 2 3 6 6 3 2 3 6Use 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.
In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.sec 5𝜋/3
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Textbook Question
In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.6 3 2 3 6 6 3 2 3 6Use 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.
In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.cos 3𝜋/2
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Textbook Question
In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.6 3 2 3 6 6 3 2 3 6Use 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.
In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.tan 3𝜋/2
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Textbook Question
In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 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)
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Textbook Question
In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 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
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Textbook Question
In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 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
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Textbook Question
In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 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
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Textbook Question
In Exercises 19–24, a. Use the unit circle shown for Exercises 5–18 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)
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Textbook Question
In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of0, 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.
sin 11𝜋/4
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Textbook Question
In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of0, 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.
cos 9𝜋/2
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Textbook Question
In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of0, 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.
tan 𝜋
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Textbook Question
In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of0, 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.
cot 15𝜋/2
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Textbook Question
In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of0, 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.sin 47𝜋/4
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Textbook Question
Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

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Textbook Question
Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

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