Question

in which quadrant would \\( \theta \\) be if \\( \cos \theta=-\frac{1}{2} \\) and \\( \tan \theta<0 \\)?
use a digit for your response rather than a roman numeral.
(1 point)
quadrant \\( \square \\)

Explanation:

Step1: Recall the sign of cosine in each quadrant

Cosine is negative in Quadrant II and III.

Step2: Recall the sign of tangent in each quadrant

Tangent \( \tan\theta=\frac{\sin\theta}{\cos\theta}\). If \(\tan\theta < 0\), then \(\sin\theta\) and \(\cos\theta\) have opposite signs.

Step3: Determine the quadrant

Since \(\cos\theta<0\) (negative), and \(\tan\theta < 0\) (so \(\sin\theta>0\) as \(\cos\theta<0\)), \(\theta\) is in Quadrant II.

Answer:

2