# 7.4 Inverses of the Trigonometric Functions

Find values of the inverse trigonometric functions.

Simplify expressions such as $({\mathrm{sin}}^{-1}x)$ and $(\mathrm{sin}x)$ .

Simplify expressions involving compositions such as $({\mathrm{cos}}^{-1}{\displaystyle \frac{1}{2}})$ without using a calculator.

Simplify expressions such as $(a/b)$ by making a drawing and reading off appropriate ratios.

The graphs of the sine, cosine, and tangent functions are shown on the following page. Are the inverses of these functions also functions? We learned earlier that a function has an inverse that is a function if it is one-to-one, which we can check with the horizontal-line test.

Note that for each function, a horizontal ...

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