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Trigonometry
Question

EXAMPLE $$1$$ Evaluating Trigonometric Functions See LarsonPrecalculus.com for an interactive version of this type of example. Evaluate the six trigonometric functions at each real number. a. $$t = \frac { \pi } { 6 }$$ b. $$t = \frac { 5 \pi } { 4 }$$ c. $$t = \pi$$ d. $$t = - \frac { \pi } { 3 }$$

a)

$$\sin ( 1 / 6 ^ { * } \pi ) = 0.5 = 1 / 2$$

$$\cos ( 1 / 6 ^ { * } \pi ) = 0.8660254 = \sqrt { 3 } / 2$$

$$\tan ( 1 / 6 ^ { * } \pi ) = 0.57735027 = 1 / \sqrt { 3 } = \sqrt { 3 } / 3$$

$$\cot ( 1 / 6 ^ { * } \pi ) = 1.73205081 = \sqrt { 3 }$$

$$\sec ( 1 / 6 ^ { * } \pi ) = 1.15470054 = 2 \sqrt { 3 } / 3$$

$$\csc ( 1 / 6 ^ { * } \pi ) = 2$$

b)

$$\sin ( 5 / 4 ^ { * } \pi ) = - 0.70710678 = - \sqrt { 2 } / 2$$

$$\cos ( 5 / 4 ^ { * } \pi ) = - 0.70710678 = - \sqrt { 2 } / 2$$

$$\tan ( 5 / 4 ^ { * } \pi ) = 1$$

$$\cot ( 5 / 4 ^ { * } \pi ) = 1$$

$$\sec ( 5 / 4 ^ { * } \pi ) = - 1.41421356 = - \sqrt { 2 }$$

$$\csc ( 5 / 4 ^ { * } \pi ) = - 1.41421356 = - \sqrt { 2 }$$

c)

$$\cos ( 1 ^ { * } \pi ) = - 1$$

$$\sec ( 1 * \pi ) = - 1$$

$$\sin ( 1 ^ { * } \pi ) = 0$$

$$\tan ( 1 ^ { * } \pi ) = 0$$

$$\cot ( 1 ^ { * } \pi ) =$$ Undefined

$$C S ( 1 ^ { * } \pi ) =$$ Undefined

d)

$$\sin ( - 1 / 3 ^ { * } \pi ) = - 0.8660254 = - \sqrt { 3 } / 2$$

$$\cos ( - 1 / 3 ^ { * } \pi ) = 0.5 = 1 / 2$$

$$\tan ( - 1 / 3 ^ { * } \pi ) = - 1.73205081 = - \sqrt { 3 }$$

$$\cot ( - 1 / 3 ^ { * } \pi ) = - 0.57735027 = - 1 / \sqrt { 3 } = - \sqrt { 3 } / 3$$

$$\sec ( - 1 / 3 * \pi ) = 2$$

$$\csc ( - 1 / 3 ^ { * } \pi ) = - 1.15470054 = - 2 \sqrt { 3 } / 3$$

Solution
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