Question

In which quadrant would θ be if cos(θ)=√3 over 2 and sin(θ)=−1 over2 ? Use a digit for your response rather than a Roman numeral. (1 point)

Answer 1

To determine the quadrant in which the angle θ lies, we need to evaluate the signs of cosine and sine.

- The value of cos(θ) = √3/2 is positive.
- The value of sin(θ) = -1/2 is negative.

In the coordinate plane, the signs of trigonometric functions correspond to the following quadrants:

1. Quadrant I: sin > 0, cos > 0
2. Quadrant II: sin > 0, cos < 0
3. Quadrant III: sin < 0, cos < 0
4. Quadrant IV: sin < 0, cos > 0

Since cos(θ) is positive and sin(θ) is negative, θ is located in Quadrant IV.

Therefore, the answer is:

4