Question

Verify the identity: cos(x+pi/2) = -sin x I think the point of this question is to use the sum/difference formula.

Answer 1

you would use the identity

cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

Answer 2

I have this so far:
cos x cos pi/2 - sin x sin pi/2 = -sin x

Answer 3

good

Answer 4

cos(pi/2) = ???

Answer 5

I have no idea. I think it's 0 but I'm not entirely sure.

Answer 6

yes, using the unit circle (get to know it or have it on a sheet of paper handy) you'll find that

cos(pi/2) = 0

sin(pi/2) = 1

Answer 7

Sooo,
cos x (0) - sin x (1) = -sin x ?

Answer 8

yep

Answer 9

the cos(x) and 0 multiply to 0

Answer 10

so the left half of cos x (0) - sin x (1) goes away

Answer 11

leaving you with

-sin(x) * 1 = -sin(x)

Answer 12

Thank you!

Answer 13

yw