Question

Find tan, csc, sec, and cot, when necessary, rationalize denominators

Answer 1

Step 1

Given;

Step 2

`\begin{gathered} tan\theta=(sin\theta)/(cos\theta)=((6)/(7))/((√(13))/(7)) \\ tan\theta=(6)/(7)*(7)/(√(13))=(6)/(√(13)) \\ tan\theta=(6)/(√(13)) \\ tan\theta=(6)/(√(13))*(√(13))/(√(13))=(6√(13))/(13) \end{gathered}`
`\begin{gathered} csc\theta=(1)/(sin(\theta)) \\ csc\theta=(1)/((6)/(7))=(7)/(6) \end{gathered}`
`sec\theta=(1)/(cos(\theta))=(1)/((√(13))/(7))=(7)/(√(13))=(7√(13))/(13)`
`cot\theta=(1)/(tan\theta)=(1)/((6√(13))/(13))=(13)/(6√(13))=(√(13))/(6)`

Answer;

`\begin{gathered} tan\theta=(6√(13))/(13) \\ csc\theta=(7)/(6) \\ sec\theta=(7√(13))/(13) \\ cot\theta=(√(13))/(6) \end{gathered}`