# How do you use transformation to graph the sin function and determine the amplitude and period of y=-2sinx?

Nov 2, 2016

The period is $2 \pi$ and the amplitude is $\pm 2$

#### Explanation:

The amplitude of $\sin \left(x\right)$ is $\pm 1$ so $2 \sin \left(x\right)$increases that to $\pm 2$
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If ${y}_{1} = \sin \left(x\right) \text{ }$then$\text{ } {y}_{2} = 2 {y}_{1} = 2 \sin \left(x\right)$
So ${y}_{2}$ is twice as big as ${y}_{1}$
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Then by changing $2 \sin \left(x\right)$ to $- 2 \sin \left(x\right)$ what was positive will be negative and what was negative will be positive.

The period does not change. What changes the period is something like $\sin \left(a x\right)$ where $a$ is a constant.

The period is $2 \pi$ and the amplitude is $\pm 2$