Consider the equation sin⁡ (2π5) = |sin⁡ x|.

Which values of x make the equation true?

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

the answer is true