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November 23, 2014

November 23, 2014

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

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 11:14amDo a search for "sum of sin cosine phase shift" and at 200clicks there's a good write-up.

In summary, with the values of r and θ given by

r = sqrt(a2 + b2 + 2ab cos(A-B))

θ = atan2(a cos A + b cos B, a sin A + b sin B),

the following expressions are equivalent:

y = a cos(x-A) + b cos(x-B)

y = r cos(x-θ)

In your case, that means that y = 17cos(theta-62) is the wave you want.

Recall that sin theta = cos(90-theta)

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