how to find exact value of trig functions

Have you ever put on an article of clothing, only to find out that it wasn't the right size?

what are inverse trig functions

Well, guess what, this same dilemma can be seen in mathematics…. albeit, not with clothing but with Inverse Trigonometric Functions!

Remember how the domain of our basic Trigonometric Functions (i.e., Sine and Cosine) are all real numbers?

And remember, how these trigonometric functions are periodic, and make a fun "wave" pattern?

Well, what we quickly realize is that these functions don't pass the Horizontal Line Test, which means they don't have inverses!

Inverse trigonometric functions

Graph of the Arcsine Function

Gasp! What are we to do?

Well, we're going to become mathematical tailors and hem our functions just like we hem an article of clothing!

What?

Ok, so we are not going to use needle and thread, but we are going to shorten the domain to make it fit just right!

Together, we are going to see how to restrict the domain of all six of our Trigonometric Functions, which are sometimes referred to as Arcfunctions, and then see how to apply this new domain, or our principle range, as Khan Academy accurately states, to our Unit Circle.

As the Math Page nicely points out, the reason why Inverse Trig Functions are commonly referred to as arcfunctions is because we are looking for the arc (i.e., the angle in radians) whose sine, cosine or tangent is the given value.

In other words, we're going to do the exact same thing we did when we learned the Unit Circle, just in reverse!

Then, we will learn how to find the exact value of an Inverse Trig Function without using a calculator by using the Unit Circle, Reference Triangles, and our Trigonometric Identities.

Inverse Trig Functions – Video

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solving inverse functions with calcworkshop