Question

identify the quadrant for the angle θ satisfying the following conditions. sin(θ)>0 and cos(θ)<0 a. quadrant iii b. quadrant iv c. quadrant i d. quadrant ii

Explanation:

Step1: Recall the sign 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 of trigonometric functions in Quadrant II.

Answer:

D. Quadrant II