Question

Which expression equivalent to: cos(theta + pi/2).
A)cos theta
B)-cos theta
C)sin theta
D)-sin theta

my book doesnt give examples of this but my crack at it would be C b/c distributive property? and 2cos theta = sin theta

Answer 1

OHHHH NOOOOO!!!!

I sure hope you don't think that
cos(A+B) = cosA + cosB !!!!!!

and what is with this 2cos theta = sin theta??

You mean like 2cos60º = sin60º
or 2(1/2) = .866 ??


We are dealing with a phase shift here, namely a shift of cos(theta) by pi/2 to the left.
So visualize cos(theta) moved 90º to the left, would you not have the standard sine curve reflected in the x-axis?
So it would be -sin(theta) which is choice D

or you can do it by using the proper expansion of cos(A+B) which is
cosAcosB - SinAsinB

cos (theta + pi/2)
= cos(theta)cos(pi/2) - sin(theta)sin(pi/2)

but cos(pi/2) = 1 and sin(pi/2) = 0

which leaves
cos(theta)cos(pi/2) - sin(theta)sin(pi/2)
= cos(theta)*0 - sin(theta)*1
= -sin(theta)

Answer 2

Good job Reiny.

Guido

Answer 3

Didn't know I was being graded, lol!

On the other hand, just give me a raise.