What is the value of sin^(-1)(1/2) + cos^(-1)(1/2)?
Practice Questions
Q1
What is the value of sin^(-1)(1/2) + cos^(-1)(1/2)?
π/3
π/2
π/6
π/4
Questions & Step-by-Step Solutions
What is the value of sin^(-1)(1/2) + cos^(-1)(1/2)?
Correct Answer: π/2
Step 1: Understand the functions involved. sin^(-1)(1/2) means 'what angle has a sine of 1/2?' and cos^(-1)(1/2) means 'what angle has a cosine of 1/2?'
Step 2: Recall the values of sine and cosine for common angles. The angle whose sine is 1/2 is π/6 (or 30 degrees).
Step 3: The angle whose cosine is 1/2 is π/3 (or 60 degrees).
Step 4: Now, add the two angles together: π/6 + π/3.
Step 5: To add these fractions, find a common denominator. The common denominator for 6 and 3 is 6.
Step 6: Rewrite π/3 as 2π/6 so that both fractions have the same denominator: π/6 + 2π/6 = 3π/6.
