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Posted by 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 - , 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 - , Friday, February 15, 2008 at 4:23pm

    Good job Reiny.

    Guido

  • Trig - , 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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