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