Inverse Trigonometric Functions
Inverse Trigonometric Functions
We touched on the inverse trigonometric functions when we were explaining how to solve right triangles. Here, we’ll go over them much more thoroughly.
The standard trig functions take an angle as input and give you the value of sine, cosine, or tangent. The inverse trig functions take a sine, cosine, or tangent value as input and give you the measure of the angle that produces that value of sine. If you know that the cosine of an angle is equal to .866, you can use the inverse cosine function to determine the measure of the angle.
The three inverse trigonometric functions you should be familiar with are sin–1, cos–1, and tan–1, which are also called arcsine, arccosine, and arctangent. For the Math IIC you simply need to know how to use these functions with your calculator. Make sure you know how to use the inverse trig functions on your calculator before the test.
Since inverse trig functions are so much fun to solve, let’s take a look at this:
What angle between – and has a tangent of –1?
You should first notice that the angles are given in radians. You must either convert these angle measures to degrees or switch to radian mode on your calculator. Next, use the tan–1 key on your calculator to measure the angle that results in a tangent value of –1. If you’ve done all this correctly, your calculator will tell you that arctan –1 = –π /4 radians = –45º. This negative angle is equal to – /4 radians or 315º.
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