Question

name the quadrant in which the angle θ lies. sinθ>0,cosθ<0 choose the correct answer below. quadrant i quadrant iv quadrant ii quadrant iii

Explanation:

Step1: Recall the signs of trigonometric functions in each quadrant

• In Quadrant I: \(\sin\theta> 0\), \(\cos\theta>0\)
• In Quadrant II: \(\sin\theta> 0\), \(\cos\theta<0\)
• In Quadrant III: \(\sin\theta< 0\), \(\cos\theta<0\)
• In Quadrant IV: \(\sin\theta< 0\), \(\cos\theta>0\)

Step2: Match the given conditions

Given \(\sin\theta>0\) and \(\cos\theta < 0\), which matches the sign - pattern of trigonometric functions in Quadrant II.

Answer:

Quadrant II