Final answer:
To find sin-1(1/2), recognize that this is asking for an angle whose sine is 1/2. This angle is well known in trigonometry as 30° or π/6 radians, which are the principal values for the inverse sine function.
Step-by-step explanation:
To find the value of sin-1(1/2), we are looking for an angle whose sine value is 1/2. In trigonometry, the inverse sine function, also known as arcsin, gives us an angle when we know the sine of that angle. Considering the unit circle and the values of sine related to well-known angles, we know that sin(30°) or sin(π/6) equals 1/2. Therefore, sin-1(1/2) = 30° or π/6 radians.
It's important to remember that the inverse sine function will return the principal value, which is the value in the range of [-π/2, π/2] for radians, or [-90°, 90°] for degrees. Since 1/2 is a positive value, the angle we want is in the first quadrant, thereby reassuring us that 30° or π/6 is the correct answer.
If you are interested in confirming these results using a calculator, be sure to set the calculator to the correct mode (degrees or radians) before calculating the inverse sine of 1/2. This can be very enlightening and help strengthen your understanding of trigonometric functions and their inverses.