Question

Write g(x) = 3cos(5x) +3sqroot3sin(5x) in terms of sine only. Please help.

Answer 1

\[b\cos(x)+a\sin(x)=\sqrt{a^2+b^2}\sin(x+\theta)\] for the appropriate \(\theta\)

Answer 2

find \(\theta\) via
\[\sin(\theta)=\frac{a}{\sqrt{a^2+c^2}}\] and
\[\cos(\theta)=\frac{b}{\sqrt{a^2+b^2}}\]

Answer 3

I get the answer 6sin(5x+pi/3) but, its wrong

Answer 4

lets see

Answer 5

yeah i screwed up that is why

Answer 6

it is
\[\cos(\theta)=\frac{a}{\sqrt{a^2+b^2}}\] and
\[\sin(\theta)=\frac{b}{\sqrt{a^2+b^2}}\]

Answer 7

this gives \(\theta=\frac{\pi}{6}\)
i had it backwards

Answer 8

thank you (: