in which quadrant would \\( \\theta \\) be if \\( \\sin \\theta = - \\frac { \\sqrt { 3 } } { 2 } \\) and…

in which quadrant would \\( \\theta \\) be if \\( \\sin \\theta = - \\frac { \\sqrt { 3 } } { 2 } \\) and \\( \\tan \\theta < 0 \\)?\nuse a digit for your response rather than a roman numeral.\n(1 point)\nquadrant \\( \\square \\)\ncheck answer remaining attempts : 3

in which quadrant would \\( \\theta \\) be if \\( \\sin \\theta = - \\frac { \\sqrt { 3 } } { 2 } \\) and \\( \\tan \\theta < 0 \\)?\nuse a digit for your response rather than a roman numeral.\n(1 point)\nquadrant \\( \\square \\)\ncheck answer remaining attempts : 3

Answer

Explanation:

Step1: Recall the sign of sine function

Sine function ( \sin\theta=\frac{y}{r}) ((r = \sqrt{x^{2}+y^{2}}>0)). If (\sin\theta<0), then (y < 0). So (\theta) is in Quadrant III or Quadrant IV.

Step2: Recall the sign of tangent function

Tangent function ( \tan\theta=\frac{y}{x}). If (\tan\theta<0), then (x) and (y) have opposite signs. Since (y < 0) (from Step 1), then (x>0).

Step3: Determine the quadrant

If (x > 0) and (y < 0), then (\theta) is in Quadrant IV.

Answer:

(4)