Question

Evaluate \( \sin 690^\circ \times \sec 240^\circ \)

• A. 1
• B. -1
• C. \( -\frac{1}{2} \)
• D. \( \frac{1}{2} \)

Hint:

When dealing with multiple angle terms, always reduce the angles by subtracting multiples of 360° if needed to simplify the calculations.

Answer 1

The Correct Option is A

Step 1: Simplify the angles.
\( \sin 690^\circ \) is equivalent to \( \sin (690^\circ - 360^\circ) = \sin 330^\circ \), and \( \sec 240^\circ \) is equivalent to \( \sec (240^\circ) = -\frac{2}{\sqrt{3}} \).
Step 2: Calculate the result.
After simplifying, we find that: \[ \sin 330^\circ = -\frac{1}{2}, \quad \sec 240^\circ = -\frac{2}{\sqrt{3}}. \] Thus, \( \sin 690^\circ \times \sec 240^\circ = 1 \).
Step 3: Conclusion.
The correct answer is (A) 1.