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Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).
Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).
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Practice Questions
1 question
Q1
Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).
π/3
π/2
π/4
2π/3
Show Solution
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sin^(-1)(√3/2) + cos^(-1)(1/2) = π/2
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate sin^(-1)(√3/2) + cos^(-1)(1/2).
Solution:
sin^(-1)(√3/2) + cos^(-1)(1/2) = π/2
Steps: 5
Show Steps
Step 1: Understand the notation. sin^(-1)(x) means the angle whose sine is x, and cos^(-1)(x) means the angle whose cosine is x.
Step 2: Find sin^(-1)(√3/2). The angle whose sine is √3/2 is π/3 (or 60 degrees).
Step 3: Find cos^(-1)(1/2). The angle whose cosine is 1/2 is π/3 (or 60 degrees).
Step 4: Add the two angles together: π/3 + π/3 = 2π/3.
Step 5: Recognize that sin^(-1)(√3/2) + cos^(-1)(1/2) is a known identity that equals π/2.
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