Question

solve 93 and 94, read directions carefully these problems are related

Answer 1

waGiven:

$\begin{gathered} (A)cos\theta=\frac{5}{13}and\text{ 0}<\theta<\frac{\pi}{2} \\ (B)sec\theta=\frac{5}{3}and\text{ }\frac{3\pi}{2}<\theta<2\pi \end{gathered}$

Find: evaluate other five function.

Explanation:(A)

$\begin{gathered} cos\theta=\frac{5}{13}=\frac{base}{hypotenuse} \\ sin\theta=\frac{12}{13} \\ cosec\theta=\frac{13}{12} \\ sec\theta=\frac{13}{5} \\ tan\theta=\frac{12}{5} \\ cot\theta=\frac{5}{12} \end{gathered}$

(B)

$\begin{gathered} sec\theta=\frac{5}{3} \\ cos\theta=\frac{3}{5} \\ sin\theta=\frac{-4}{5} \\ cosec\theta=\frac{-5}{4} \\ tan\theta=\frac{-4}{3} \\ cot\theta=\frac{-3}{4} \end{gathered}$$\begin{gathered} cos\theta=\frac{5}{13}=\frac{base\text{ }}{hypotanuse} \\ \\ \end{gathered}$

by phythagorean property ,

$\begin{gathered} (13)^2=(5)^2+x^2 \\ x^2=169-25 \\ x^2=144 \\ x=12 \end{gathered}$