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Trigonometry
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

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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