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.

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- Sep 14th 2010, 04:23 AMTwoPlusTwoExact 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. - Sep 14th 2010, 04:33 AMProve It
$\displaystyle \sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}$.

- Sep 14th 2010, 05:00 AMTwoPlusTwo
- Sep 14th 2010, 05:14 AMProve It
You know that $\displaystyle \sin{x} = \frac{1}{3}$.

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

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

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

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

$\displaystyle = \frac{2\sqrt{2}}{3}$. - Sep 14th 2010, 05:38 AMTwoPlusTwo
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!