Question

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

Answer 1

Step 1

Given;

Step 2

$\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta}=\frac{\frac{6}{7}}{\frac{\sqrt{13}}{7}} \\ tan\theta=\frac{6}{7}\times\frac{7}{\sqrt{13}}=\frac{6}{\sqrt{13}} \\ tan\theta=\frac{6}{\sqrt{13}} \\ tan\theta=\frac{6}{\sqrt{13}}\times\frac{\sqrt{13}}{\sqrt{13}}=\frac{6\sqrt{13}}{13} \end{gathered}$$\begin{gathered} csc\theta=\frac{1}{sin(\theta)} \\ csc\theta=\frac{1}{\frac{6}{7}}=\frac{7}{6} \end{gathered}$$sec\theta=\frac{1}{cos(\theta)}=\frac{1}{\frac{\sqrt{13}}{7}}=\frac{7}{\sqrt{13}}=\frac{7\sqrt{13}}{13}$$cot\theta=\frac{1}{tan\theta}=\frac{1}{\frac{6\sqrt{13}}{13}}=\frac{13}{6\sqrt{13}}=\frac{\sqrt{13}}{6}$

Answer;

$\begin{gathered} tan\theta=\frac{6\sqrt{13}}{13} \\ csc\theta=\frac{7}{6} \\ sec\theta=\frac{7\sqrt{13}}{13} \\ cot\theta=\frac{\sqrt{13}}{6} \end{gathered}$