Final answer:
To use the unit circle for finding exact values of inverse trigonometric functions, locate the angle in the appropriate quadrant whose sine or cosine value matches the given value. For inverse cosine, use Quadrants I and II; for inverse sine, use Quadrants I and IV.
Step-by-step explanation:
To find the exact values of inverse trigonometric functions using the unit circle, we must first recall that the inverse cosine (\(\arccos\)) function will yield an angle whose cosine is the input value, and is restricted to Quadrants I and II. Likewise, the inverse sine (\(\arcsin\)) function yields an angle whose sine is the input value, and is restricted to Quadrants I and IV.
For example, if we want to calculate the inverse cosine of 1/2, we need to find an angle whose cosine value is 1/2. Looking at the unit circle in Quadrants I and II, we find this angle to be \(\frac{\pi}{3}\) rad or 60 degrees. Similarly, for the inverse sine of 1/2, we seek an angle in Quadrants I and IV. The angle with a sine value of 1/2 is \(\frac{\pi}{6}\) rad or 30 degrees, which is in Quadrant I.