Write the trigonometric expression as an algebraic expression in U

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October 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...
October 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 $\theta=\arctan(U)$ , then $\tan(\theta)=U$ .
So what is $\cos(\theta)=~?$
October 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?
October 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 $\tan(\theta)=3$ what $\cos(\theta)=~?$
October 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
October 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 $\tan(\theta)=3$ that you cannot tell us what value $\cos(\theta)$ has.

If you cannot, then no wonder you don't know how do this question.
October 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 $\tan(\theta) = u, ~ \cos(\theta) = ?$ 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.