Determine the quadrant of θ if cosθ=3√2 and tanθ=−3√3 .(1 point) Responses Quadrant III Quadrant III Quadrant I Quadrant I Quadrant II Quadrant II Quadrant IV Quadrant IV

Answer 1

To determine the quadrant of \( \theta \) given \( \cos \theta = 3\sqrt{2} \) and \( \tan \theta = -3\sqrt{3} \), we can analyze the signs of the trigonometric functions:

1. Cosine: \( \cos \theta \) is positive.
2. Tangent: \( \tan \theta \) is negative.

Now, we identify in which quadrants cosine is positive and tangent is negative:

• Quadrant I: \( \cos \theta > 0 \), \( \tan \theta > 0 \) (not applicable)
• Quadrant II: \( \cos \theta < 0 \), \( \tan \theta > 0 \) (not applicable)
• Quadrant III: \( \cos \theta < 0 \), \( \tan \theta < 0 \) (not applicable)
• Quadrant IV: \( \cos \theta > 0 \), \( \tan \theta < 0 \) (applicable)

Since \( \cos \theta \) is positive and \( \tan \theta \) is negative, \( \theta \) must be in Quadrant IV.

Therefore, the answer is:

Quadrant IV