Question

If sin θ = -(1)/(2) and tan θ = 1√(3), then θ is equal to:

• A. 2π + (π)/(6)
• B. 2π + (11π)/(6)
• C. 2π + (7π)/(6)
• D. 2π + (π)/(4)

Hint:

Use signs of trigonometric functions to locate quadrant.

Answer 1

The Correct Option is C

Step 1: Signs of trigonometric ratios. sin θ < 0 and tan θ > 0 implies third quadrant.
Step 2: Reference angle. sin 30^ = (1)/(2) θ = 210^ = (7π)/(6)
Step 3: General solution. θ = 2π + (7π)/(6)