Questions: Determine the quadrant in which θ lies. sec (θ) > 0, cot (θ) < 0 I II III IV

Determine the quadrant in which θ lies. sec (θ) > 0, cot (θ) < 0 I II III IV
Transcript text: Determine the quadrant in which $\theta$ lies. \[ \sec (\theta)>0, \cot (\theta)<0 \] I II III IV
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Solution

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Solution Steps

Step 1: Identify the Trigonometric Function(s) and Their Signs
  • The sign of sec is positive.
  • The sign of cot is negative.
Step 2: Use the ASTC Rule to Determine Possible Quadrants
  • For sec being positive, possible quadrants are: 1, 4.
  • For cot being negative, possible quadrants are: 2, 4.
Step 3: Match the Signs to the Quadrants

Final Answer: Based on the given conditions, the angle lies in Quadrant 4.

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