Posted by Bryan on Sunday, December 9, 2007 at 5:31pm.
I don't think any formula is necessary. I believe it just wants the equivalent angle measurement. In that case, pi is 180 degrees. Therefore, pi/24 would be 180/24, which can be simplified. I'm not 100% sure if this is the form they are requesting, though.
They want it in this form.
sin (pi/6) is 1/2
So sin (pi/240 is ______
Well, converting to degrees it is 7.5 degrees
that makes me think right off that 30 degrees divided by two is 15 degrees and 15 degrees divided by two is 7.5 degrees
so I have a sneaking suspicion that if I divide 30 degrees by two twice I will get pi/24
but 30 degrees is pi/6
and we know that sin(pi/6) = 1/2
and cos pi/6 = sqrt3/2
All of which is my hard way of saying that we can get there from
pi/24 = (1/2)(1/2) (pi/6)
and we know the sin and cos of pi/6 exactly
I think Bryan did not copy the question correctly. I agree with Michael that the way it stands it is not much of a question.
pi/24 cannot be stated "exactly" since pi is a transcendental number
Probably the question said
find the exact value of sin pi/24 or
find the exact value of cos pi/24
I will do the cos pi/24
As Damon noted pi/24 radians is 7.5º, or 1/2 of 1/2 of 30º whose cosine we know to be √3/2
so starting with cos 30 = 2cos^2 15º - 1
if got cos 15º = √(√3+2)/2
and then cos 15º = 2cos^2 7.5º - 1
√(√3+2)/2 = 2cos^2 7.5º - 1
which after "simplifying" gave me
cos 7.5º = √(√(√3 + 2) + 2)/2
cos pi/24 = √(√(√3 + 2) + 2)/2
check
cos 7.5º = .9914448
Right Side of my equation = .9914448
so pi/24 = cos^-1[ √(√(√3 + 2) + 2)/2 ]
I guess :)
certainly, of course, lol
Ya sorry it was sin (pi/24)