Thread: exact values

Find the exact value of sin(−7pi/12):

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

intp


the half angle identity lets you stuff that into


Can you solve from there?

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

ok....so do you know how to turn into an exact answer?

Assuming you do, the answer is

so plugging that into the equation, you get

simplifying, you get

that then get simplified further to

and finally


the initial equation is , which puts it in 3rd quadrant, so we know it needs to be negative, or


Is it clearer?

yes thank you!

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

Originally Posted by samtheman17

Find the exact value of sin(−7*pi/12):

Alternatively, note that







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

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.