Question

If sec \(\theta\) = 2, then the value of \(\theta\) will be

• A. 90°
• B. 60°
• C. 45°
• D. 30°

Hint:

It's highly beneficial to memorize the trigonometric values for standard angles (0°, 30°, 45°, 60°, 90°) for all six ratios (sin, cos, tan, cosec, sec, cot). This allows for instant recall and saves valuable time during exams.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question requires knowledge of the values of trigonometric ratios for standard angles (0°, 30°, 45°, 60°, 90°).
Step 2: Key Formula or Approach:
The secant function is the reciprocal of the cosine function: \( \sec \theta = \frac{1}{\cos \theta} \). We can use this relationship to find the value of \( \cos \theta \) and then determine the angle \(\theta\).
Step 3: Detailed Explanation:
We are given:
\[ \sec \theta = 2 \] Using the reciprocal identity:
\[ \cos \theta = \frac{1}{\sec \theta} = \frac{1}{2} \] We need to find the angle \(\theta\) (for \(0^\circ \le \theta \le 90^\circ\)) for which \( \cos \theta = \frac{1}{2} \).
From the standard trigonometric values, we know that:
\[ \cos 60^\circ = \frac{1}{2} \] Therefore, the value of \(\theta\) is 60°.
Step 4: Final Answer:
The value of \(\theta\) is 60°.