Question

V3

Answer 1

Question:

The angle $\theta_1$ is located in Quadrant III, and $sin(\theta_1) = - \sqrt{\frac{3}{2}}$.

What is the value of $cos(\theta_1)$ ?

Express your answer exactly. $cos(\theta1) =$ ________

Answer:

$cos(\theta_1) = - \frac{1}{2}$

Step-by-step explanation:

Given:

$sin(\theta_1) = - \sqrt{\frac{3}{2}}$

Since the angle $\theta_1$ is located in Quadrant III, we have:

$sin(\theta_1) = sin(\pi + \frac{\pi}{3})$

$\theta_1 = \pi + \frac{\pi}{3}$

$\theta_1 = \frac{4 \pi}{3}$

Thus, $cos(\theta_1)$ =

$cos(\theta_1) = cos(\pi + \frac{\pi}{3})$

$cos(\theta_1) = -cos(\frac{\pi}{3})$

$cos(\theta_1) = - \frac{1}{2}$