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 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)

## Answer This Question

## Related Questions

- Calculus - I wanted to confirm that I solved these problems correctly (we had to...
- 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...
- math - I have a question I have been working on since yesterday and I am not ...
- 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