# Trig Identity/Pre-Calc help

• Dec 18th 2008, 04:00 PM
Dust
Trig Identity/Pre-Calc help
I have a problem as follows:

cos((π/3) - X)

I then used the addition identity of cos(x-y) = cos x cos y + sin x sin y and got:

cos(π/3)*cosX + sin(π/3)*sinX

Then i used the unit circle to get

(1/2)*cosX + √(3)*sinX

And am now stuck. I'm supposed to solve for 'x' but i'm not sure how to continue.
-I'm supposed to use trig identities, of course.

I posted this in both urgent hw help and pre-calc because its both urgent and in pre-calc (Itwasntme). I'll remove one as soon as either get a reply.
• Dec 18th 2008, 04:16 PM
Skalkaz
Dear Dust,

what is your problem?? You wrote a simple expression not an equation or else.

Bye the way, once again how many sin(pi/3) ?
• Dec 18th 2008, 04:47 PM
Dust
I have to solve for x. Thats the problem - I don't know how to further simplify to the point where i can solve X.

And .. just one pi/three? I don't understand your question; sorry.

Its just cos of (pi/3) minus the variable x
• Dec 18th 2008, 05:01 PM
fonso_gfx
Quote:

Originally Posted by Dust

cos(π/3)*cosX + sin(π/3)*sinX

(1/2)*cosX + √(3)*sinX

There is an error above

it should be
$\displaystyle \frac{1}{2}cos(x) + \frac{\sqrt{3}}{2}Sin(x) = \frac{cos(x) +\sqrt{3}Sin(x)}{2}$

maybe that's why you got stuck

• Dec 18th 2008, 05:06 PM
Skalkaz
solve, solve, but what??
You wrote an expression: cos(pi/3 - x) without sign '='.
Man can usually solve an equation, e. g. 2x = 10
but only 2x is meaningless to solve.

My question: sin(pi/3) = ?
• Dec 18th 2008, 05:25 PM
Dust
Skalkaz - the point of this problem is to solve for x. so the problem equals whatever x is. But you don't know it till you solve it so it doesn't really matter.

Thank you, Fonso.
• Dec 18th 2008, 05:38 PM
Dust
How do you continue solving this problem?
• Dec 18th 2008, 05:46 PM
Skalkaz
No problem. (Lipssealed)
• Dec 18th 2008, 06:05 PM
Prove It
Quote:

Originally Posted by Dust
Skalkaz - the point of this problem is to solve for x. so the problem equals whatever x is. But you don't know it till you solve it so it doesn't really matter.

Thank you, Fonso.

Skalkaz is exactly right, you can't solve an equation for x without an equation.

You have given the left hand side

$\displaystyle \cos{(\frac{\pi}{3} - x)}$

Now you need an equals sign and a right hand side.

Then we can solve.