Answer: -4/5
Step-by-step explanation:
Ok so cos(x) = -4/5 and we know that:
.
If we plug that in and solve for sin(x) we get:
Now we have to consider: <em>is sin(x) positive or negative?</em>
We have that .
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: <em>what is ?</em>
Here's where another important equation comes in:
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