An inverse trig function is simply a trig function done backwards. When you're finding the value of a trigonometry function, you provide an angle, and the trig function gives you a ratio. In an inverse trigonometry function, you provide the ratio, and the function gives you the angle.

For example, since the sine of 30 degrees is 0.5, the inverse sine of 0.5 is 30 degrees.

Of course, it's going to be cumbersome to say "inverse sine of" all the time, so we need a way to abbreviate that. We write it this way:

sin^-1 x

where x is the ratio that we want to find the angle for.

Many calculators provide the inverse trig functions as the 2nd function of the regular trig function buttons.

Sample #1
Find sin^-1 0.1.

Solution
Use the inverse sine function on your calculator to obtain: sin^-1 0.1 = 5.74 degrees

Sample #2
In right triangle ABC (right angle at C) a = 20 and c = 30. What is the measure of angle A?

Solution
sin^-1 20 / 30 = 41.8 degrees

For the problems below, refer to the following diagram: