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MatroZZZ [7]
3 years ago
10

V3

Mathematics
1 answer:
valentinak56 [21]3 years ago
3 0

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}

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