Question

name the quadrant in which the angle \\( \theta \\) lies.
\\( \sin \theta>0, \cos \theta<0 \\)

choose the correct answer below.

\\( \bigcirc \\) quadrant i
\\( \bigcirc \\) quadrant iii
\\( \bigcirc \\) quadrant ii
\\( \bigcirc \\) quadrant iv

Explanation:

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

Since \(\sin\theta>0\) (positive) and \(\cos\theta < 0\) (negative), we refer to the sign - rules of trigonometric functions in each quadrant.

Answer:

Quadrant II