# What is the domain and range of y =arccos(sin(2x))?

##### 1 Answer
Nov 29, 2016

The domain is $\mathbb{R}$ and the range is $\left[0 , \pi\right]$

#### Explanation:

The domain of the function $\arccos y$ is the interval $\left[- 1 , 1\right]$.

As $- 1 \le \sin \left(2 x\right) \le 1 \forall x \in \mathbb{R}$

The function $\arccos \left(\sin \left(2 x\right)\right)$ is defined for every $x$.

Besides, $\sin \left(2 x\right)$ assumes every possible value in the domain of $\arccos y$ so the range of the function is the same as the natural range of $\arccos$, that is the interval $\left[0 , \pi\right]$.