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

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)

Good job Reiny.

Guido

Didn't know I was being graded, lol!

On the other hand, just give me a raise.

To find the expression equivalent to cos(theta + pi/2), we can use the trigonometric identity:

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

By substituting theta in place of x, we can determine the equivalent expression:

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

Therefore, the correct answer is option D) -sin theta.

To understand this concept further, you can use the unit circle or the definitions of sine and cosine in the right triangle. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. It can help us visualize the values of sine and cosine for different angles.

For each point on the unit circle, the x-coordinate is equal to cos(theta), and the y-coordinate is equal to sin(theta). When we add pi/2 radians to an angle theta, we effectively rotate counterclockwise by 90 degrees. This rotation changes the cosine to the negative sine (-sin(theta)).