Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).

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Question: Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).

Options:

Correct Answer: π

Solution:

2sin^(-1)(1/2) = 2(π/6) = π/3 and 2cos^(-1)(1/2) = 2(π/3) = 2π/3. Therefore, the total is π/3 + 2π/3 = π.

Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).

Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).

Step 1: Identify the expression to evaluate: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).
Step 2: Calculate sin^(-1)(1/2). This is the angle whose sine is 1/2. The angle is π/6.
Step 3: Multiply the result from Step 2 by 2: 2 * (π/6) = π/3.
Step 4: Calculate cos^(-1)(1/2). This is the angle whose cosine is 1/2. The angle is π/3.
Step 5: Multiply the result from Step 4 by 2: 2 * (π/3) = 2π/3.
Step 6: Add the results from Step 3 and Step 5: π/3 + 2π/3 = (1π + 2π)/3 = 3π/3 = π.
Step 7: The final result of the expression is π.

Inverse Trigonometric Functions – Understanding the values of sin^(-1) and cos^(-1) for specific inputs.
Angle Addition – Combining angles derived from inverse trigonometric functions.
Radians vs Degrees – Recognizing the importance of using radians in trigonometric calculations.