Question

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

Which values of x make the equation true?

Answer 1

the answer is true

Explanation:

Answer 2

x = -2π5, x = 2π5

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...

1. sin⁡(2π5) = sin⁡(x)
2. 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