SOLUTION: Suppose a genius figured out that sin(7pi/12)= -((sqrt(2)+sqrt(60)/4) Find each of the following exactly (show steps) a). sin (-(7pi/12)) b.) sin (-(5pi/12)) c. cos

Question 570994: Suppose a genius figured out that
sin(7pi/12)= -((sqrt(2)+sqrt(60)/4)
Find each of the following exactly (show steps)
a). sin (-(7pi/12))
b.) sin (-(5pi/12))
c. cos(pi/12)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
It does not take a genius to find the exact value of , but having those trigonometric identity formulas handy helps.
The expression you posted for is wrong. Either someone made a typo somewhere, or the person who wrote the problem is trying to confuse us all.
Since the expression given for looked fishy to me, I went looking for the trigonometric identity formulas to find the correct exact value of .
It turns out that
HOW I CALCULATED THAT (just in case you care)
I found the trigonometric identity

and that was useful, because I know that
so
and everybody knows that

and

So
=

BACK TO THE PROBLEM
I am going to use
However, it turns out that all the answers are either that expression, or (-1) times that, so if you were meant to use the fishy expression, you'll easily figure out the intended answers
a) so

b) so and are supplementary angles. They add up to , which is .
And we know that
so
and
c)
I think we are expected to go to that table of trigonometric identities to find

Luckily, as everybody knows, and
So
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