3. Unit Circle

Use the unit circle shown to find the value of the trigonometric function.

cos 𝜋/6

Use the unit circle shown to find the value of the trigonometric function.

sin (2𝜋/3)

Use the unit circle shown to find the value of the trigonometric function.

tan 11𝜋/6

The unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋

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.

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sin 3𝜋/2

The unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋/4, 𝜋/2, 3𝜋/4, 𝜋, 5𝜋/4, 3𝜋/2, 7𝜋/4, and 2𝜋.

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.

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sin 3𝜋/4

Find each exact function value. ​See Example 3.

sin π/3

Find each exact function value. ​See Example 3.​

tan π/4

Find each exact function value. ​See Example 3.​

sec π/6

Find each exact function value. ​See Example 3.​

sin π/2

Find each exact function value. ​See Example 3.​

tan 5π/3