EXAMPLE $1$ Evaluating Trigonometric Functions S...

Question

$EXAMPLE $1$ Evaluating Trigonometric Functions S...$

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. $t = - \frac { \pi } { 3 }$

Answer

$\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$

$\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 }$

$\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

$\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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