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Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).
Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).
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Practice Questions
1 question
Q1
Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).
π
2π
π/2
0
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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.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).
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.
Steps: 7
Show Steps
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.
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