20 April, 08:14
Consider the equation sin (2π5) = |sin x|.
Which values of x make the equation true?
20 April, 08:51
the answer is true
20 April, 09:07
x = - 2π5, x = 2π5
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
Know the Answer?
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» Consider the equation sin (2π5) = |sin x|. Which values of x make the equation true?