Write the following in terms of sin θ and cos θ; then simplify if possible. (Leave your answer in terms of sin θ and/or cos θ.)
sin θ cot θ + 8 cos θ

Question

Write the following in terms of sin θ and cos θ; then simplify if possible. (Leave your answer in terms of sin θ and/or cos θ.)
sin θ cot θ + 8 cos θ

liziekay · Answer

@zepdrix

zepdrix · Answer

Eyyyy Lisa May.

Remember how to turn cotangent into sines and cosines?

liziekay · Answer

Well, I know that tan = sin theta/ cos theta

zepdrix · Answer

k good.
cotangent is the flip of tangent.
so cot = cos / sin

zepdrix · Answer

$$\large\rm \sin \theta\color{orangered}{\cot \theta}+8\cos \theta$$becomes,$$\large\rm \sin \theta\color{orangered}{\frac{\cos \theta}{\sin \theta}}+8\cos \theta$$That's a good first step, ya?

liziekay · Answer

agreed

zepdrix · Answer

Hmm what next?
Any ideas?

misssmartiez · Answer

That awkward moment when a person asks something that you have no clue about.


*cringes*

I'll go with zepdrix. I don't really exceed much in math. I'd stick to L-arts, English, and science for now.

liziekay · Answer

I don't think we can elliminate any variables

liziekay · Answer

but sin is 1/csc theta so maybe that helps?

zepdrix · Answer

No?
Remember than when you have something sitting on it's own,
it's the same as having it in the numerator,$$\large\rm a\frac{b}{c}=\frac{ab}{c}$$

zepdrix · Answer

No, we've sines and cosines, let's leave it that way.
We have a cancellation somewhere though.
Not seeing it yet?

liziekay · Answer

right! I totally blanked out. You could elliminate sin theta!

liziekay · Answer

would it be 9 cos since you have two of them?

zepdrix · Answer

1cos +8cos left over after cancellation?
And combining like-terms?

Yayy good job!

liziekay · Answer

That was quite simple, I was way over thinking it!!