7-6 Inverse Trig Functions

Okay, so today I am going to explaing to you how to solve inverse trig functions. There are four easy steps to solve these problems.

These four steps are:

1. The first thing you would do is isolate the trig function.
2. The next thing is to take the inverse of the trig function, for example sin would be sin -1.
3. You would then use the trig chart or calculator to find the answers.
4. The last step is to use the quadrans to find the right angle.

Note: There is always going to be at least two answers for each inverse.

--When you move quadrants to find your answers you would do the following:

• To go to quadrant 1 to 2, you would make the angle negative and add 180 degrees.
• To go to quadrant 1 to 3, you would just simply add 180 degrees.
• To go to quadrant 1 to 4, you would make the angle negative and add 360 degrees.

Now I am going to do an example of these types of problems.

Example 1: sin-1(.9)

1. The trig function is already isolated.
2. It already gives you the inverse of the function, so you don't need to do anything for this step.
3. Since .9 is not on the trig chart you would plug that into your calculator to find the degree. You would then get 64.158 degrees.
4. Since sin is y/r and .9 is positive, you are going to find angles in quadrant 1 and 2. 64.158 degrees is already in quadrant one so all you would have to do is convert that into degrees, minutes, and seconds, which would be 64 degrees 9 minutes and 28 seconds. Next you would want to find an angle in quadrant 2. According to the note above, to move from quadrant 1 to 2 you would make your angle negative and add 180. This would then give you 115.842, you would then convert that into degrees, minutes, and seconds, which would give you 115 degrees 50 minutes and 31 seconds.

Your answer would then be your two angles which are: 64 degrees 9 minutes 28 seconds and 115 degrees 50 minutes 31 seconds.

--Halie!