Question

Find the exact values of the six trigonometric functions of each angle 8.

Answer 1

Given: The trigonometry shown in the image

To Determine: The exact values of the six trogonometric functions of each angle shown

Solution

It can be observed that

Therefore

`\begin{gathered} sin\theta=-1 \\ cos\theta=-√(2) \end{gathered}`
`tan\theta=(sin\theta)/(cos\theta)=(-1)/(-√(2))=(1)/(√(2))`
`\begin{gathered} csc\theta=(1)/(sin\theta)=(1)/(-1)=-1 \\ sec\theta=(1)/(cos\theta)=(1)/(-√(2))=-(1)/(√(2)) \\ cot\theta=(1)/(tan\theta)=(1)/((1)/(√(2)))=1*√(2)=√(2) \end{gathered}`