Question

Use an appropriate formula to write 5*sin 15 degrees * cos 25 degrees- 5*cos 15 degrees * sin 25 degrees as k sin theta or k cos theta, with suitable cvalues for k and theta. Theta must be positive, k can be positive or negative. Do not evaluate.

What...

Answer 1

Use the formula
\[
\sin(a-b)= \sin(a) \cos(b) - \cos(a) \sin(b)
\]

Answer 2

So sin(15degrees-25degrees)? but what about the 5 before the first sin and second cosine?

Answer 3

\[
\sin( 15-25) = \sin(15) \cos(25) - \cos(15) \sin(25)\\
5\sin( -10) =5 \sin(15) \cos(25) - 5\cos(15) \sin(25)\\
-5\sin(10) =5 \sin(15) \cos(25) - 5\cos(15) \sin(25)\\
k=-5\\
\theta=10
\]

Answer 4

Multiply the two sides by 5