Posted by Nathaniel. B on Sunday, November 13, 2011 at 4:56pm.
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.

Math  Steve, Monday, November 14, 2011 at 11:14am
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)
Answer This Question
Related Questions
 Calculus  I wanted to confirm that I solved these problems correctly (we had to...
 math  I have a question I have been working on since yesterday and I am not ...
 science  Sitting on a horizontal track is a mass of 10kg. One end of the track ...
 Precalculs  I have no idea how to do these type of problems. Problem...
 Trigonometry  Prove the following identities: 1. (tan theta  sin theta)^2 + (1...
 Trigonometry  Prove the following identities: 1. (tan theta  sin theta)^2 + (1...
 Algebra II  Multiple Choice Which expression is NOT equivalent to 1? (theta) ...
 math(Trigonometry)  sin 2 theta + cos theta = 0 so, we use sin 2 theta = 2 sin ...
 trig  Hi, I need to find the domain and rnge of the following: 1. X= 1/2 (cos ...
 Trigonometry  Use a sum of difference identity to write the expression as a ...
More Related Questions