# Thread: Determining the exact value of each expression

1. ## Determining the exact value of each expression

Hi guys, I'm having trouble with obtaining the correct results for this expression.

The question is: Determine the exact value of each expression.

[cos(pi/4)tan(5pi/6)] / [sin(3pi/4)]

Somehow, I obtained the answer square root of three... but the answer is supposed to be square root of 6 divided by 6.

2. Are you sure either answer is right, or that you copied the problem correctly?

I get an answer of $\displaystyle -\frac{\sqrt3}{3}$.

$\displaystyle \frac{(\frac{\sqrt2}{2})\cdot(-\frac{\sqrt3}{3})}{(\frac{\sqrt2}{2})}$

3. Originally Posted by Henderson
Are you sure either answer is right, or that you copied the problem correctly?

I get an answer of $\displaystyle -\frac{\sqrt3}{3}$.

$\displaystyle \frac{(\frac{\sqrt2}{2})\cdot(-\frac{\sqrt3}{3})}{(\frac{\sqrt2}{2})}$
Ditto what Henderson said

4. Oh no! I didn't copy it right! It's supposed to be cos(4pi/3) instead of cos(pi/4)

5. well, you should know that $\displaystyle \cos\left(\frac{4\pi}{3}\right) = -\frac{1}{2}$

sub it in for the $\displaystyle \frac{\sqrt{2}}{2}$ in the numerator of the expressions given and re-evaluate.

6. how did you get square root of 2 over 2 as the denominator tho?

-cos(pi/3) = -1/2
-tan(pi/6) = - 1/ square root of 3
sin(pi/4) = 1/ square root of 2

7. $\displaystyle \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$

8. i mean.. how did you get your answer? the answer that i got wat 2/(2*square root of 3)