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Please please helpplpplpol

Please please helpplpplpol-example-1
User Rob Porter
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1 Answer

2 votes

Answer: -4/5

Explanation:

Ok so cos(x) = -4/5 and we know that:


sin^2(x) + cos^2(x) = 1.

If we plug that in and solve for sin(x) we get:


sin^2(x) = (9)/(25) \\sin(x) = (3)/(5)

Now we have to consider: is sin(x) positive or negative?

We have that
\pi &nbsp;< x < (3\pi )/(2).

From the unit circle, we know that sin(x) is negative in this range. Therefore sin(x) actually equals -3/5.

But the question asks: what is
sin(x + (\pi )/(2))?

Here's where another important equation comes in:


sin(\alpha &nbsp;+ \beta ) = sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)

In this case, we have alpha = x and beta = pi/2.

So, that looks like:

sin(x + pi/2 )= sin(x)cos(pi/2) + cos(x)sin(pi/2)

We already have what sin(x) and cos(x) are. We also know that sin( pi/2) = 1 and cos(pi/2) = 0.

sin(x + pi/2 ) = (-3/5)(0) + (-4/5)(1).

Therefore we simply have

sin(x + pi/2) = -4/5

User Danko
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