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.
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 $\displaystyle \cos{x} = \sqrt{1 - \left(\frac{1}{3}\right)^2}$
$\displaystyle = \sqrt{1 - \frac{1}{9}}$
$\displaystyle = \sqrt{\frac{8}{9}}$
$\displaystyle = \frac{2\sqrt{2}}{3}$.