Step 1: Understand what sin(π/3) means. It is the sine of the angle π/3 radians.
Step 2: Calculate sin(π/3). The value of sin(π/3) is √3/2.
Step 3: Now, we need to find sin^(-1)(√3/2). This means we are looking for the angle whose sine is √3/2.
Step 4: The angle that has a sine of √3/2 is π/3 radians.
Step 5: Check if π/3 is within the range of the inverse sine function, which is from -π/2 to π/2. Since π/3 is approximately 1.047, it is within this range.
Step 6: Since π/3 is in the range of sin^(-1), we conclude that sin^(-1)(sin(π/3)) = π/3.
Inverse Trigonometric Functions – Understanding how the inverse sine function (sin^(-1)) operates within its defined range.
Principal Values of Trigonometric Functions – Recognizing that the output of sin^(-1)(x) is restricted to the range [-π/2, π/2].
