# How do you find the domain and range of y = sin(2x)?

Oct 25, 2017

Domain: $\left(- \infty , + \infty\right)$
Range: $\left[- 1 , + 1\right]$

#### Explanation:

$y = \sin \left(2 x\right)$

$y$ is defined $\forall x \in \mathbb{R}$

$\therefore$ the domain of $y$ is $\left(- \infty , + \infty\right)$

Let $\theta = 2 x$

$y = \sin \theta \to - 1 \le y \le + 1 \forall \theta \in \mathbb{R}$

Hence, $y = \sin \left(2 x\right) \to - 1 \le y \le + 1 \forall \theta \in \mathbb{R}$

$\therefore$ the range of $y$ is $\left[- 1 , + 1\right]$

We can observe the domain and range of $y$ from the graph of y=sin(2x) below.

graph{sin(2x) [-6.25, 6.234, -3.12, 3.124]}

Oct 25, 2017

Domain: $- \infty < x < \infty \mathmr{and} x | \left(- \infty , \infty\right)$
Range: −1 ≤ y≤ 1 or [-1.1]

#### Explanation:

$y = \sin \left(2 x\right)$ , the domain of the function y=sin(2x) is all real

numbers (sine is defined for any angle measure),

i.e $- \infty < x < \infty \mathmr{and} x | \left(- \infty , \infty\right)$

The range is −1 ≤ y≤ 1 or [-1.1] , as maximum and minimum

value of $y$ lie in between $- 1$ and $1$ , inclusive.

Domain: $- \infty < x < \infty \mathmr{and} x | \left(- \infty , \infty\right)$

Range: −1 ≤ y≤ 1 or [-1.1]#

graph{sin(2x) [-10, 10, -5, 5]} [Ans]