Lang Herrera
02/18/2024 · Primary School

\( \sin s=0.7660 \) (Round to four decimal places as needed.) \( \cos s=0.6428 \) (Round to four decimal places as needed.) Base on the values of \( \sin \mathrm{s} \) and \( \cos \mathrm{s} \), in which quadrant is an angle of s radians located?

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To determine the quadrant in which the angle \( s \) is located based on the values of \( \sin s \) and \( \cos s \), we can analyze the signs of these trigonometric functions. 1. **Given Values**: - \( \sin s = 0.7660 \) (positive) - \( \cos s = 0.6428 \) (positive) 2. **Quadrant Analysis**: - In the **first quadrant** (Quadrant I), both sine and cosine are positive. - In the **second quadrant** (Quadrant II), sine is positive and cosine is negative. - In the **third quadrant** (Quadrant III), both sine and cosine are negative. - In the **fourth quadrant** (Quadrant IV), sine is negative and cosine is positive. Since both \( \sin s \) and \( \cos s \) are positive, the angle \( s \) must be located in **Quadrant I**.

Quick Answer

The angle \( s \) is located in Quadrant I.
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