sin(x) > 1/2" in "[0,2pi)?

How do I solve for x

1 Answer
Apr 2, 2018

pi/6 < x < {5pi}/6

Explanation:

Keep in mind that sinx is always greater than or equal to zero and less than or equal to 1.
0 leq sinx leq 1. That being said we have the following range: 1 geq sinx > 1/2

Looking at the unit circle we can see that when sinx =1/2, x=pi/6 or x={5pi}/6. This gives us a range of pi/6 < x < {5pi}/6

When sinx=1, x = pi/2
This is already within the range of pi/6 < x < {5pi}/6 so we do not need to explicitly include that in our range.