# Exact value (trig)

• September 14th 2010, 04:23 AM
TwoPlusTwo
Exact value (trig)
How do I find the exact value of an expression like this one?

u=sin(x+pi/4)

when sin(x)= 1/3 and x is in the range 0-90 degrees.

Thanks.
• September 14th 2010, 04:33 AM
Prove It
$\sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}$.
• September 14th 2010, 05:00 AM
TwoPlusTwo
Quote:

Originally Posted by Prove It
$\sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}$.

Yeah, that’s what I thought, but what should I do when I have this?

u=(√2/2)sin(x) + (√2/2)cos(x)
• September 14th 2010, 05:14 AM
Prove It
You know that $\sin{x} = \frac{1}{3}$.

You should also know that $\cos{x} = \sqrt{1 - \sin^2{x}}$ from the Pythagorean Theorem.

That means $\cos{x} = \sqrt{1 - \left(\frac{1}{3}\right)^2}$

$= \sqrt{1 - \frac{1}{9}}$

$= \sqrt{\frac{8}{9}}$

$= \frac{2\sqrt{2}}{3}$.
• September 14th 2010, 05:38 AM
TwoPlusTwo
Allright! Got it now. I assume you mean:

cos(x)=√1-cos^2(x)

Which makes:

cos(x)=√8/3 not √10/3

That gave me the right answer. Thanks!