# Math

posted by .

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)

## Similar Questions

1. ### science

Sitting on a horizontal track is a mass of 10kg. One end of the track is raised untill the mass just begins to slip. If the coeffieient of static friction is .4 what is the minimum angle at which the mass begins to slip?
2. ### Calculus

I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
3. ### Precalculs

I have no idea how to do these type of problems. -------Problem-------- Solve each equation on the interval 0 less than or equal to theta less than 2 pi 42. SQRT(3) sin theta + cos theta = 1 ---------------------- There is an example …
4. ### Algebra II

Multiple Choice Which expression is NOT equivalent to 1?
5. ### trig

Hi, I need to find the domain and rnge of the following: 1. X= 1/2 (cos theta + theta sin theta) Y=1/2 (sin theta - theta cos theta) total guess here, but here goes Domain cos theta = +/- 1 and domain sin theta = +/- 1 so domain theta …
6. ### math(Trigonometry)

sin 2 theta + cos theta = 0 so, we use sin 2 theta = 2 sin theta cos theta right?
7. ### math

I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = -2/3, which of the following are possible?
8. ### Trigonometry

Use a sum of difference identity to write the expression as a single function theta: cos(theta - pi). Okay so I know we will use cosAcosA+sinBsinB I got: cos(theta)cos(theta)sin(pi)sin(pi) I don't know how to solve from here and I'm …
9. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
10. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …

More Similar Questions