1. ## COMPASS trigonometry question

Hi, I'm taking the a Math placement test this Saturday so I've been practicing for that, but here's a problem I just can't figure out:

If sin(x+y) = sinx cosx + cosx siny
find sin((pi/2)+αlpha).
The answer to this is supposed to be cos aplha, but I'm not sure how you get there.

I found a similar problem in one of my Math books so I substituted
((pi/2)+alpha) for x and y in the equation above. I got

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

then I went on to divide by sin(pi/2) and sin alpha

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

the left side will cancel, right? So we have

1 = cos alpha + cos (pi/2)

pi/2 = 90degrees and cos 90degrees = 0, right?

so then

1 = cos alpha

Is that correct? what about the 1 on the left side? Can I just leave it there?

2. Originally Posted by tami-chan87
Hi, I'm taking the a Math placement test this Saturday so I've been practicing for that, but here's a problem I just can't figure out:

If sin(x+y) = sinx cosx + cosx siny
find sin((pi/2)+αlpha).
The answer to this is supposed to be cos aplha, but I'm not sure how you get there.

I found a similar problem in one of my Math books so I substituted
((pi/2)+alpha) for x and y in the equation above. I got

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

then I went on to divide by sin(pi/2) and sin alpha

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

the left side will cancel, right? So we have

1 = cos alpha + cos (pi/2)

pi/2 = 90degrees and cos 90degrees = 0, right?

so then

1 = cos alpha

Is that correct? what about the 1 on the left side? Can I just leave it there?
No you made you mistake when you divided by (sin(pi/2) + sin(alpha))

(Besides that, your division is completely wrong.)

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

sin((pi/2)+alpha) = (1) cos alpha + (0) sin alpha = cos (alpha)