# F(x) = sin(-3x) increase decrease intervals

#### vaze

Hi everyone.

Could anyone help me solve this. I need to find the increase and decrease intervals of f(x) = sin(-3x).

The increase intervals of sin(x) are $-\pi/2 + 2\pi*k < x < \pi/2 + 2\pi*k$

Is the following the right way to solve my problem (for increase intervals)? $-\pi/2 + 2\pi*k < -3x < \pi/2 + 2\pi*k$
By multiplying by -3 you get: $-\pi/6 + 2/3\pi*k < x < \pi/6 + 2/3\pi*k$ (1)

Although when plotting sin(-3x) this interval (1) is the decrease one. Why?

#### mathman

sin(-3x)=-sin(3x). Work with this form, since you don't have to work with things going in opposite directions.

#### vaze

How would you use sin(x) = -sin(x) in this problem?

#### HomogenousCow

How would you use sin(x) = -sin(x) in this problem?
If sin(x) is increasing then -sin(x) is decreasing, vice versa.

#### vaze

Yes, thank you. I have already solved it this way. My textbook had an error in the solutions sheet. They just solved the double inequality and did not exchange the increase and decrease intervals.

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