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20 April, 08:14

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

Which values of x make the equation true?

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Answers (2)
  1. 20 April, 08:51
    0
    the answer is true
  2. 20 April, 09:07
    0
    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
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