Problem

Identify all possible quadrants of an angle $\theta$ that satisfies the given conditions. \[ \cos \theta=0, \tan \theta<0 \] Select all possible quadrants below. A. Quadrant II B. Quadrant IV C. Quadrant I D. Quadrant III

Solution

Step 1 :The cosine of an angle is zero when the angle is \(\frac{\pi}{2}\) or \(\frac{3\pi}{2}\) (90 or 270 degrees). This means that the angle is either in Quadrant II or Quadrant III.

Step 2 :However, the tangent of an angle is negative when the angle is in Quadrant II or Quadrant IV.

Step 3 :Therefore, the only quadrant that satisfies both conditions is Quadrant II.

Step 4 :\(\boxed{\text{Quadrant II}}\)

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Source: https://solvelyapp.com/problems/7632/

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