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

Answer

Expert–verified

Hide Steps

Answer

$\boxed{\text{Quadrant II}}$

Steps

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 ：$\boxed{\text{Quadrant II}}$

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 IIB. Quadrant IVC. Quadrant ID. Quadrant III

Answer

Popular Problems

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