Question

Let $(-3,-4)$ be a point on the terminal side of $\theta$.Find the sine ,cosine, and tangent of $\theta$

Answer 1

Let us that, $\theta$ is the angle made by the line joining origin and the given point $(-3,-4)$, with respect to the x axis. Then the given point will lie on the terminal side of the $\theta$.

Therefore,

$\tan \theta =\frac{-4}{-3}=\frac{4}{3}$.

$\cos \theta =\frac{1}{\sqrt{1+{\tan }^2\theta }}$

$=\frac{3}{\sqrt{9+16}}=\frac{3}{5}$.

$\sin \theta =\sqrt{1-{\cos }^2\theta }$

$=\frac{4}{5}$

since the point is in the third quadrant, both $\sin \theta$ and $\cos \theta$ will be negative, while $\tan \theta$ will be positive.

Hence

$\sin \theta =\frac{-4}{5}$

$\cos \theta =\frac{-3}{5}$

$\tan \theta =\frac{4}{3}$