Homework Help: Trig

Posted by Jon on Friday, February 15, 2008 at 2:23pm.

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

Trig - Reiny, Friday, February 15, 2008 at 2:45pm
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)
Trig - Guido, Friday, February 15, 2008 at 4:23pm
Good job Reiny.

Guido
- Trig - Reiny, Friday, February 15, 2008 at 4:55pm
  Didn't know I was being graded, lol!
  
  On the other hand, just give me a raise.

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