1 Answer

Anthney · Answer 1 · 2021-03-19T15:37:04+0000

Question:

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

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

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

Answer:

$cos(\theta_1) = - (1)/(2)$

Explanation:

Given:

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

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

$sin(\theta_1) = sin(\pi + (\pi)/(3))$

$\theta_1 = \pi + (\pi)/(3)$

$\theta_1 = (4 \pi)/(3)$

Thus,
$cos(\theta_1)$ =

$cos(\theta_1) = cos(\pi + (\pi)/(3))$

$cos(\theta_1) = -cos((\pi)/(3))$

$cos(\theta_1) = - (1)/(2)$

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