Use a sum of difference identity to write the expression as a single function theta: cos(theta - pi).
Okay so I know we will use cosAcosA+sinBsinB
I got:
cos(theta)cos(theta)sin(pi)sin(pi)
I don't know how to solve from here and I'm not sure if that is correct.
You got your formula a bit garbled.
cos(A-B) = cosAcosB + sinAsinB
Recalling some well-known values, that is
cosθ cosπ + sinθ sinπ
= cosθ(-1) + sinθ(0)
= -cosθ
But then, you know that from working with reference angles in the various quadrants, right?
To write the expression cos(theta - pi) using a sum of difference identity, we can use the following identity:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
In this case, we want to express the expression cos(theta - pi) in terms of a single function of theta. So, we can let A = theta and B = pi.
Substituting the values into the identity, we get:
cos(theta - pi) = cos(theta)cos(pi) + sin(theta)sin(pi)
Now, we can simplify further. The cosine of pi is -1, and the sine of pi is 0. Therefore, we can substitute these values into the expression:
cos(theta - pi) = cos(theta)(-1) + sin(theta)(0)
Since sin(pi) = 0, the second term becomes zero. Thus, the expression further simplifies to:
cos(theta - pi) = -cos(theta)
Therefore, the final expression as a single function of theta is -cos(theta).