Question

Verify the identity
cos(x+pi/2)= -sinx

Answer 1

Use the sum formula for the cosine function:\[\cos (a+b) = \cos a \cos b - \sin a \sin b\]

Look up cos pi/2 and sin pi/2.

Answer 2

im sorry im a little confused

Answer 3

The identity I gave you is always true. Substitute x for a and pi/2 for b.

Write out the identity after having done this. Use the fact that sin pi/2=1 to simplify your equation. Also use the fact that cos pi/2=0 to simplify it.

Answer 4

Just to make you're not confused :
cos(x + pi/2) =
cos x cos pi/2 - sin x sin pi/2 =
cos x cos 90 - sin x sin 90 =
cos x (0) - sin x (1) =
0 - sin x =
-sin x

Answer 5

Thank you, everyone