Question

Use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

Answer 1

we have

$\begin{gathered} tan(30^o)=\frac{1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\ therefore \\ tan(30^o)=\frac{\sqrt{3}}{3} \end{gathered}$$\begin{gathered} csc45^o=\frac{1}{sin45^o} \\ \\ sin45^o=\frac{1}{\sqrt{2}} \\ \\ csc45^o=\frac{1}{\frac{1}{\sqrt{2}}} \\ \\ csc45^o=\sqrt{2} \end{gathered}$$\begin{gathered} cot\frac{\pi}{3}=\frac{1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\ \\ cot\frac{\pi}{3}=\frac{\sqrt{3}}{3} \end{gathered}$$\begin{gathered} tan\frac{\pi}{4}+csc\frac{\pi}{6}=\frac{1}{1}+\frac{1}{\frac{1}{2}}=1+2=3 \\ therefore \\ tan\frac{\pi}{4}+csc\frac{\pi}{6}=3 \end{gathered}$