h t t p : / / w w w . j i s k h a . c o m / d i s p l a y . c g i ? i d = 1 2 5 8 1 5 2 7 6 5
In that one you asked for
sin ( - pi/12)
csc ( (25 pi)/12)
1. first of all, sin(-A) = -sin(A)
so sin(-pi/12) = -sin(pi/12)
Perhaps you find it easier to think of these in degrees ?
pi/12 = 15º
let's use the identity
cos2A = 1 - 2sin^2 A
cos 30º = 1 - 2sin^2 15º
√3/2 = 1 - 2sin^2 15
2sin^2 15 = 1 -√3/2
sin^2 15 = (2-√3)/4
sin 15 = √(2-√3)/2
sin(-pi/12) = -√(2-√3)/2
2. csc ( (25 pi)/12)
Again, let's think in degrees
25pi/12 radians = 375º = 360º + 15º
so it is coterminal with 15º
but we just found sin 15 = √(2-√3)/2
so csc 15º = csc (25pi/12) = 2/√(2-√3)
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