Answer:
x = -2π5, x = 2π5
Step-by-step explanation:
The absolute value sign just mean that both the negative and positive value in the |...| would give you the answer. Remember how |7|=7 and |-7|=7 too?
In this case
sin(2π5) = |sin x|
is the same as...
- sin(2π5) = sin(x)
- sin(2π5) = -sin(x)
solve for x in these two cases.
In case (1) sin(2π5)= sin(x)
sin(2π5) = sin(x)
The stuff inside the parentheses must e the same so x=2π5.
In case (2) sin(2π5) = -sin(x)
A property of sine is that it's an odd function. This means you can move the negative sign outside the parentheses and put it inside: sin(-x) = -sin(x). So lets do that to our problem.
sin(2π5) = -sin(x)
sin(2π5) = sin(-x)
as we can see, the stuff inside the parentheses must be so the same, so
2π5 = -x
-2π5 = x
