# How do you find the remaining trigonometric functions of theta given tantheta=3/4 and theta terminates in QIII?

Sep 5, 2017

$\frac{3}{5} , \frac{5}{3} , \frac{4}{5} , \frac{5}{4} , \frac{4}{3}$

#### Explanation:

We know tan$\theta$ = 3/4 = height/base of a right angle triangle.

Hence, hypotenuse = $\sqrt{b a s {e}^{2} + h e i g h {t}^{2}}$ = $\sqrt{{4}^{2} + {3}^{2}}$

= $\sqrt{25} = 5$

Hence sin$\theta = \left(\text{height")/("hypotenuse}\right) = - \frac{3}{5}$
cosec$\theta = \frac{1}{\sin} \theta = - \frac{5}{3}$.
cos$\theta = \left(\text{base")/("hypotenuse}\right) = - \frac{4}{5}$
sec$\theta = \frac{1}{\cos} \theta = - \frac{5}{4}$
cot$\theta = \frac{1}{\tan} \theta = \frac{4}{3}$