Friday

April 18, 2014

April 18, 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)

**Related Questions**

Math - I think this is geometry: There is a small box with a black frame around ...

accounting - Can someone give me the site where I can do practice problems for ...

math - This isn't a specific math question. I'm just looking for some tips for ...

math - i know the square root of 36 is 6 but wat if their was a negative sign in...

Physics - A sealed box containing a chunk of ice is made of 2cm thick wood, a ...

Apple Computer - I chose this as another product to answer questions on. The ...

Physics - A closed box is filled with dry ice at a temperature of -81.5 C, while...

Geometry - There is a 48 inch cereal box lying on the floor. It was placed ...

Math - If you are calculating the capacity of material that will fit inside a ...

Physics - *I really don't know how to get started. I have done lots of the ...