Math
posted by Nathaniel. B on .
One of the "think outside the box" problems in my math work is really challenging me.
I need to write and equation expressing:
8 cos theta + 15 sin theta as a single sinusoid
I tried graphing to no avail and there is nothing in my textbook about turning an equation like that into a sinusoidal equation.

Do a search for "sum of sin cosine phase shift" and at 200clicks there's a good writeup.
In summary, with the values of r and θ given by
r = sqrt(a2 + b2 + 2ab cos(AB))
θ = atan2(a cos A + b cos B, a sin A + b sin B),
the following expressions are equivalent:
y = a cos(xA) + b cos(xB)
y = r cos(xθ)
In your case, that means that y = 17cos(theta62) is the wave you want.
Recall that sin theta = cos(90theta)