Question

if tan(θ)=-15/8 and sin(θ) is positive find other 5trig ratio and determine which quodrants θ in

Answer 1

$\tan (\theta)=\frac{opposite}{_{\text{ }}adjacent}$

Since the sine is positive, we can conclude:

Opposite = 15

Adjacent = -8

Therefore, the angle θ is in the II quadrant, and the other 5 trigonometric functions are given by:

$\begin{gathered} \sin (\theta)=\frac{opposite}{_{\text{ }}hypotenuse} \\ _{\text{ }}where\colon \\ _{\text{ }}hypotenuse=\sqrt[]{15^2+(-8)^2} \\ _{\text{ }}hypotenuse=17 \\ so\colon \\ \sin (\theta)=\frac{15}{17} \end{gathered}$$\cos (\theta)=\frac{adjacent}{_{\text{ }}hypotenuse}=-\frac{8}{17}$$\csc (\theta)=\frac{_{\text{ }}hypotenuse}{_{\text{ }}opposite}=\frac{17}{15}$$\sec (\theta)=\frac{_{\text{ }}hypotenuse}{_{\text{ }}adjacent}=-\frac{17}{8}$$\cot (\theta)=\frac{adjacent}{_{\text{ }}opposite}=-\frac{8}{15}_{}$