# Write the trigonometric expression as an algebraic expression in U

• Oct 6th 2011, 12:36 PM
Nervous
Write the trigonometric expression as an algebraic expression in U
cos(arctan U)

I seriously had this down until my teacher stopped using numbers...
• Oct 6th 2011, 12:50 PM
Plato
Re: Write the trigonometric expression as an algebraic expression in U
Quote:

Originally Posted by Nervous
cos(arctan U)

Let $\displaystyle \theta=\arctan(U)$, then $\displaystyle \tan(\theta)=U$.
So what is $\displaystyle \cos(\theta)=~?$
• Oct 6th 2011, 01:01 PM
Nervous
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?
• Oct 6th 2011, 01:11 PM
Plato
Re: Write the trigonometric expression as an algebraic expression in U
Quote:

Originally Posted by Nervous
Cos(Theta) = cos(arctan(U))
But that doesn't get me anywhere...?

Oh come on. THINK!
If $\displaystyle \tan(\theta)=3$ what $\displaystyle \cos(\theta)=~?$
• Oct 6th 2011, 01:30 PM
Nervous
Re: Write the trigonometric expression as an algebraic expression in U
Where does 3 come from? And I editted my post since you replied
• Oct 6th 2011, 01:45 PM
Plato
Re: Write the trigonometric expression as an algebraic expression in U
Quote:

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 $\displaystyle \tan(\theta)=3$ that you cannot tell us what value $\displaystyle \cos(\theta)$ has.

If you cannot, then no wonder you don't know how do this question.
• Oct 6th 2011, 01:48 PM
mr fantastic
Re: Write the trigonometric expression as an algebraic expression in U
Quote:

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 $\displaystyle \tan(\theta) = u, ~ \cos(\theta) = ?$ to try and guide you to answering the general question. You are meant to realise that.

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

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