1. ## exact values

Find the exact value of sin(−7pi/12):

2. Originally Posted by samtheman17
yes it is
So, the way I'd do this is using the half angle trig identity for Sin. So that turns
$sin\frac{-7\pi}{12}$
intp
$sin\frac{-7\pi}{6}$

the half angle identity lets you stuff that into
$\pm \sqrt{\frac{1-cos\frac{-7\pi}{6}}{2}}$

Can you solve from there?

3. hmm......im still unsure what to do from this point

4. ok....so do you know how to turn $cos\frac{-7\pi}{6}$ into an exact answer?

Assuming you do, the answer is $\frac{-\sqrt{3}}{2}$

so plugging that into the equation, you get
$\pm\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$
simplifying, you get
$\pm\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$
that then get simplified further to
$\pm\sqrt{\frac{2+\sqrt{3}}{4}}$
and finally
$\pm\frac{\sqrt{2+\sqrt{3}}}{2}$

the initial equation is $sin\frac{-7\pi}{12}$, which puts it in 3rd quadrant, so we know it needs to be negative, or
$-\frac{\sqrt{2+\sqrt{3}}}{2}$

Is it clearer?

5. yes thank you!

can that be simplified any further though??
just out of curiosity....

6. Originally Posted by samtheman17
Find the exact value of sin(−7*pi/12):
Alternatively, note that

$\sin \frac {-7 \pi}{12} = - \sin \frac {7 \pi}{12}$

$= - sin \left( \frac {4 \pi}{12} + \frac {3 \pi}{12} \right)$

$= - sin \left( \frac {\pi}3 + \frac {\pi}4 \right)$

Now apply the addition formula for sine, and don't forget that you have a negative sign out in front...

7. that's the most simple exact answer. You could actually solve it and get a decimal value, but it wouldn't be exact any more since you'd have to round it. The (inaccurate) decimal answer is like -0.9659258263.... but if this is for class and your professor/teacher is anything like mine, giving a decimal answer would result in a fail.

*edit* Good call Jhevon. There are certainly other ways to solve this equation.