Question

Write the linear combination of cosine and sine as a single cosine with a phase displacement: y=12cos(theta)+5sin(theta)

Answer 1

I think i got it, but can you check my work? >.>

Answer 2

\[y=12\cos \theta+5\sin \theta \]
b=12, c=5;
\[A=\sqrt{144+25}\]
\[A=13\]
D=arctan(12/5)
=tan^-1(12/5)+180*n where n belongs to the integers. Because both cosine and sine are positive, the quadrant the angle terminates in is QI.
\[y=13\cos( \theta -67.38013505...*)\]