Find the value of sin^(-1)(√3/2) + sin^(-1)(1/2).

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Question: Find the value of sin^(-1)(√3/2) + sin^(-1)(1/2).

Options:

Correct Answer: π/2

Solution:

sin^(-1)(√3/2) = π/3 and sin^(-1)(1/2) = π/6. Therefore, π/3 + π/6 = π/2.

Find the value of sin^(-1)(√3/2) + sin^(-1)(1/2).

Find the value of sin^(-1)(√3/2) + sin^(-1)(1/2).

Step 1: Identify the values of sin^(-1)(√3/2) and sin^(-1)(1/2).
Step 2: Recall that sin^(-1)(√3/2) is the angle whose sine is √3/2. This angle is π/3 (or 60 degrees).
Step 3: Recall that sin^(-1)(1/2) is the angle whose sine is 1/2. This angle is π/6 (or 30 degrees).
Step 4: Add the two angles together: π/3 + π/6.
Step 5: To add π/3 and π/6, find a common denominator. The common denominator for 3 and 6 is 6.
Step 6: Convert π/3 to sixths: π/3 = 2π/6.
Step 7: Now add the two fractions: 2π/6 + π/6 = (2π + π)/6 = 3π/6.
Step 8: Simplify 3π/6 to π/2.

Inverse Trigonometric Functions – Understanding the values of sin^(-1) for common angles.
Angle Addition – Adding angles in radians to find the resultant angle.