# How do I solve #sin(5x-pi/3)<=0, [-pi/2,pi/2]#?

##### 1 Answer

Given:

First, do this without the domain restriction.

This is true when the primary values of the argument are:

Add

Add integer multiples of

Divide everything by 5:

I have graphed the domain restriction:

Please observe that there are 3 values of n, -1, 0 and 1, that fall within the domain but the leftmost (n = -1) will be truncated by the domain's lower bound:

n = -1:

The union of the 3 domain segments is the solution to the inequality with the domain restriction.