Question

Let \( \cot \theta = -5/12 \) where \( \frac{\pi}{2} < \theta < \pi \). Then the value of \( \sin \theta \) is

• A. \(-\frac{12}{13}\)
• B. \(-\frac{5}{13}\)
• C. \(\frac{12}{13}\)
• D. \(\frac{5}{13}\)
• E. \(\frac{7}{13}\)

Hint:

Use quadrant signs carefully in trigonometry problems.

Answer 1

The Correct Option is C

Concept: \[ \cot \theta = \frac{\cos\theta}{\sin\theta} \]

Step 1: Convert to triangle. \[ \cot\theta = -\frac{5}{12} \Rightarrow \tan\theta = -\frac{12}{5} \]

Step 2: Use quadrant. \[ \frac{\pi}{2}0,\cos<0 \]

Step 3: Construct triangle. Opp = 12, Adj = -5 Hypotenuse: \[ \sqrt{144+25}=13 \]

Step 4: Compute sine. \[ \sin\theta = \frac{12}{13} \]