Express in terms of x:sin(...

I have such a problem:

a) Find

(Make sure your answer is an algebraic expression with square roots but without trigonometric or inverse trigonometric functions.)

Well, I have got the answer (how could I not, with a calculator it wasn't a big deal)

but I'm not sure about this question - I don't really understand what I need to do?

b) Express in terms of

do I have to plug in the value obtained in a) or what

, doesn't make sense for me...

Re: Express in terms of x:sin(...

I'd consider (b) as separate problem. Here is the trick. Let

So now you can proceed algebraically using trig identities, or geometrically and make your own right triangle. Tangent = opposite over adjacent, and so you can make a right triangle where one of the acute angles is , the opposite side is and the adjacent side is . You can use Pythagoras to find the other side. With the fully populated triangle, you can find all trig functions of . Would you know how to proceed?

Re: Express in terms of x:sin(...

BTW, for part (a), your calculator gave you an algebraic answer or a decimal expansion? Because you were asked for the former.

Re: Express in terms of x:sin(...

Quote:

Originally Posted by

**Jhevon** I'd consider (b) as separate problem. Here is the trick. Let

So now you can proceed algebraically using trig identities, or geometrically and make your own right triangle. Tangent = opposite over adjacent, and so you can make a right triangle where one of the acute angles is

, the opposite side is

and the adjacent side is

. You can use Pythagoras to find the other side. With the fully populated triangle, you can find all trig functions of

. Would you know how to proceed?

OK, so by Pthagorian's we have the hypotenuse = , but further...

we would have am I right... do I need to do something else?

Re: Express in terms of x:sin(...

Quote:

Originally Posted by

**Jhevon** BTW, for part (a), your calculator gave you an algebraic answer or a decimal expansion? Because you were asked for the former.

dose that mean that I wasn't supposed to use the calculator, I'm working in webwork and, anyways, if I enter expressions in form of radicals and fractions it gives me the equivalent in decimal expansion - I obtained the decimal expansion,

was I supposed to apply the same method that you showed me for b) ?

Re: Express in terms of x:sin(...

Hello, dokrbb!

Here's the first one . . .

Let .[1]

Let .[2]

We have: .

Substitute [1] and [2]: .

Multiply by

Multiply by

. . . . . .

. . . . . .

Re: Express in terms of x:sin(...

that's perfect, thanks a lot - and I already figured how to do the second one: I used