Question:
The angle [tex] \theta_1[/tex] is located in Quadrant III, and [tex] sin(\theta_1) = - \sqrt{\frac{3}{2}} [/tex].
What is the value of [tex] cos(\theta_1)[/tex] ?
Express your answer exactly. [tex] cos(\theta1) = [/tex] ________
Answer:
[tex] cos(\theta_1) = - \frac{1}{2} [/tex]
Step-by-step explanation:
Given:
[tex] sin(\theta_1) = - \sqrt{\frac{3}{2}} [/tex]
Since the angle [tex] \theta_1[/tex] is located in Quadrant III, we have:
[tex] sin(\theta_1) = sin(\pi + \frac{\pi}{3}) [/tex]
[tex] \theta_1 = \pi + \frac{\pi}{3}[/tex]
[tex] \theta_1 = \frac{4 \pi}{3}[/tex]
Thus, [tex] cos(\theta_1) [/tex] =
[tex] cos(\theta_1) = cos(\pi + \frac{\pi}{3}) [/tex]
[tex] cos(\theta_1) = -cos(\frac{\pi}{3}) [/tex]
[tex] cos(\theta_1) = - \frac{1}{2} [/tex]
