Friday

December 19, 2014

December 19, 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)

**Answer this Question**

**Related Questions**

Calculus - I wanted to confirm that I solved these problems correctly (we had to...

Precalculs - I have no idea how to do these type of problems. -------Problem...

science - Sitting on a horizontal track is a mass of 10kg. One end of the track ...

algebra - Can someone please help me do this problem? That would be great! ...

math - I have a question I have been working on since yesterday and I am not ...

math(Trigonometry) - sin 2 theta + cos theta = 0 so, we use sin 2 theta = 2 sin ...

Diagonalize - construct a nondiagonal 2 x 2 matrix that is diagonalizable but ...

math - Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t...

calculus - conic sections prove that the line x-2y+10=0 touches the ellipse 9x^2...

trig - Hi, I need to find the domain and rnge of the following: 1. X= 1/2 (cos ...