Trig

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

  1. 👍
  2. 👎
  3. 👁
  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)

    1. 👍
    2. 👎
  2. Good job Reiny.

    Guido

    1. 👍
    2. 👎
  3. Didn't know I was being graded, lol!

    On the other hand, just give me a raise.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact values of sin(theta), csc(theta), and cot(theta). 2. Let (theta) be an angle in quadrant IV such that sin(theta)=-2/5. Find the exact values of sec(theta)

  2. Algebra 2

    Simplify the trigonometric expression. sin^2 theta / 1-cos theta A. 1+cos theta B. sin theta C. 1-sin theta / cos theta D. 1+sin theta / cos theta

  3. Precalculus

    Which of the following are trigonometric identities? Select all that apply (there are 3 answers). A cos^2(theta)=sin^2(theta)-1 B sin(theta)=1/csc(theta) C sec(theta)=1/cot(theta) D cot(theta)=cos/sin(theta) E

  4. Pre-Calculus

    1.) Which of the following polar equations is equivalent to the parametric equations below? x=t^2 y=2t A.) r=4cot(theta)csc(theta) B.) r=4tan(theta)sec(theta) C.) r=tan(theta)sec(theta)/4 D.) r=16cot(theta)csc(theta) 2.) Which

  1. trig

    If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.

  2. Precalculus check answers help!

    1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.)

  3. Math

    Cos square theta divided by 1-tan theta +sin cube theta divided by sin theta -cos theta = 1+sin theta *cos theta

  4. Precalculus

    Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the

  1. Trig

    Find the exact value of sin2(theta) if cos(theta) = -sqrt 5/3 and 180 < theta < 270. A)-1/9 B)-4 sqrt 5/9 C)1/9 D)4 sqrt 5/9 B? sin^2(theta) + cos^2(theta) = 1 sin^2(theta) = 1 - cos^2(theta) sin^2(theta) = 1 - (sqrt 5/3)^2

  2. math;)

    What is a simplified form of the expression (sec^3 theta) - (sec theta/cot^2 theta)? a. 0 b. sec theta-tan theta c. cos theta d. sec theta***** Every time I attempt to work out this problem I end up with one. I know the answer is

  3. Trigonometry

    1. sin^2 theta+cos theta=2 (Hint: Use the Pythagorean identity sin^2 theta+cos theta=1 to replace sin^2 theta in the given equation.) I got no solution

  4. Trig(3 all with work)

    1)Find the exact value of cos 105 by using a half-angle formula. A)sqrt 2 - sqrt 3 /2 B)-sqrt 2 - sqrt 3 /2 C)-sqrt 2 + sqrt 3 /2 D)sqrt 2 + sqrt 3 /2 cos 105 cos 105 = cos 210/2 sqrt 1 + 210/2 sqrt 1 + sqrt 3/2 /2 sqrt 2 + sqrt

You can view more similar questions or ask a new question.