# Determine the quadrant of the angle’s terminal line lies Sin x = -0.45 & cos x < 0 ?

Jun 6, 2018

The angle lies in quadrant 3 .

#### Explanation:

$\sin x = - 0.45$

Because $\sin x$ is negative, angle (arc) $x$ lies either in Q3 or Q4.

Because $\cos x < 0$, $x$ lies in Q. 3.

Note:
Calculator gives 2 values of x:
$x = - {26.74}^{\circ}$ and
$x = 180 - \left(- 26.74\right) = 180 + 26.74 = {206.74}^{\circ}$
$x = {206.74}^{\circ}$ is the answer.

$x$ lies in Quadrant 3, and
$\cos \left(206.74\right)$ is negative.