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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 -

    Do 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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