Question

If theta= -11 pi 6 then find exact values for the following

Answer 1

`\begin{gathered} sec\theta=(2)/(√(3)) \\ csc\theta=2 \\ tan\theta=(1)/(√(3)) \\ cot\theta=√(3) \end{gathered}`

Explanations;

Given the following theta value shown;

`\theta=-(11\pi)/(6)`
`\begin{gathered} sec\theta=(1)/(cos\theta) \\ sec(-(11\pi)/(6))=(1)/(cos(-(11\pi)/(6))) \\ sec(-(11\pi)/(6))=(1)/((√(3))/(2)) \\ sec(-(11\pi)/(6))=(2)/(√(3)) \\ \end{gathered}`
`\begin{gathered} csc(\theta)=(1)/(sin\theta) \\ csc(-(11\pi)/(6))=(1)/(sin(-(11\pi)/(6))) \\ csc((11\pi)/(6))=(1)/(sin(-(11\pi)/(6))) \\ csc(-(11\pi)/(6))=(1)/(0.5) \\ csc(-(11\pi)/(6))=2 \end{gathered}`
`\begin{gathered} tan\theta=tan(-(11\pi)/(6)) \\ tan(-(11\pi)/(6))=(1)/(√(3)) \end{gathered}`
`\begin{gathered} cot\theta=(1)/(tan\theta) \\ cot(-(11\pi)/(6))=(1)/(((1)/(√(3)))) \\ cot(-(11\pi)/(6))=√(3) \end{gathered}`