Question

Find the value of the following expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) \]

• A. \( \frac{1}{2} \)
• B. \( 1 \)
• C. \( \frac{3}{4} \)
• D. \( \frac{1}{4} \)

Hint:

Remember: Use standard trigonometric values to simplify expressions involving sine and cosine.

Answer 1

The Correct Option is A

Step 1: Use known trigonometric values We know the following standard values for sine and cosine: \[ \sin(30^\circ) = \frac{1}{2}, \quad \cos(60^\circ) = \frac{1}{2} \] Step 2: Substitute the values into the expression Substitute \( \sin(30^\circ) = \frac{1}{2} \) and \( \cos(60^\circ) = \frac{1}{2} \) into the expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) = \left( \frac{1}{2} \right)^2 + \left( \frac{1}{2} \right)^2 = \frac{1}{4} + \frac{1}{4} = \frac{1}{2} \] Answer: The correct answer is option (1): \( \frac{1}{2} \).