# Trigonometric Function

Consider the unit circle, $x_{2}+y_{2}=1$. We have $x=cosθ$ $y=sinθ$

See Trigonometric Identities for useful properties.

### Working with Sines and Cosines

In some applications of calculus to physics and engineering, we’ll have input information of the form $g(t)=Asin(ωt+α)$ but we’ll find that our mathematical analysis will result in output of the form $g(t)=asinωt+bcosωt$ We use the [[notes/Trigonometric Identities#Sum and Difference Formulas|Trigonometric Identities#Sum and Difference Formulas]] to equate the two and solve for $α$ and $A$.

### Inverse Trigonometric Functions

Inverse trig functions don’t actually exist, since no periodic function can have an inverse (because periodic functions can’t be one-to-one). Inverse trig functions are inverses of versions of the trigonometric functions which have restrictions imposed on their domains.

Inverse Sine Function $y=sin_{−1}x,y∈[2−π ,2π ]$ Inverse Cosine Function $y=cos_{−1}x,y∈[0,π]$ Inverse Tangent Function $y=tan_{−1}x,y∈(2−π ,2π )$