# Thread: Write the trigonometric expression as an algebraic expression in U

1. ## Write the trigonometric expression as an algebraic expression in U

cos(arctan U)

I seriously had this down until my teacher stopped using numbers...

2. ## Re: Write the trigonometric expression as an algebraic expression in U

Originally Posted by Nervous
cos(arctan U)
Let $\theta=\arctan(U)$, then $\tan(\theta)=U$.
So what is $\cos(\theta)=~?$

3. ## Re: Write the trigonometric expression as an algebraic expression in U

Cos(Theta) = cos(arctan(U))
Cos(Tan(theta))= Cos(U)
ArcCos(Tan(theta))=U

Yes?

4. ## Re: Write the trigonometric expression as an algebraic expression in U

Originally Posted by Nervous
Cos(Theta) = cos(arctan(U))
But that doesn't get me anywhere...?
Oh come on. THINK!
If $\tan(\theta)=3$ what $\cos(\theta)=~?$

5. ## Re: Write the trigonometric expression as an algebraic expression in U

Where does 3 come from? And I editted my post since you replied

6. ## Re: Write the trigonometric expression as an algebraic expression in U

Originally Posted by Nervous
Where does 3 come from?
Well, in the OP you complained about not having numbers.

Are you saying that if someone tells you that $\tan(\theta)=3$ that you cannot tell us what value $\cos(\theta)$ has.

If you cannot, then no wonder you don't know how do this question.

7. ## Re: Write the trigonometric expression as an algebraic expression in U

Originally Posted by Nervous
Where does 3 come from? And I editted my post since you replied
Where the 3 comes from is that Plato is giving you a concrete example of the general question $\tan(\theta) = u, ~ \cos(\theta) = ?$ to try and guide you to answering the general question. You are meant to realise that.

Answer Plato's question ( $\tan(\theta) = 3, ~ \cos(\theta) = ?$) and then consider how you might use it as a guide to answering $\tan(\theta) = u, ~ \cos(\theta) = ?$

Also, please don't edit posts after getting replies. For obvious reasons it just creates confusion.