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Olin [163]
3 years ago
11

Consider the equation sin⁡ (2π5)=|sin⁡ x|. Which values of x make the equation true?

Mathematics
2 answers:
aleksley [76]3 years ago
7 0

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...

  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

ElenaW [278]3 years ago
6 0

Answer:

the answer is true

Step-by-step explanation:

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