1. x = sqrt (3) / 2 y = 1/2 r = 1
So
sine = y / r = 1/2 csc = 2
cosine = x / r = [ sqrt(3) / 2] sec = 2 / sqrt(3)
tangent = y/x = sqrt(3) cotangent = x /y = 1/ sqrt(3) = sqrt(3) / 3
2. x = -2/5 y = sqrt(21) / 5 r = 1
sine = sqrt(21)/5 csc = 5/sqrt(21) = [5/21]*sqrt(21)
cosine = -2/5 sec= -5/2
tangent = -sqrt(21)/2 cotangent = -2 / sqrt(21) = [-2/21] * sqrt(21)
3. x = [2sqrt(2)] /3 y = - 1/3 r = 1
sine = -1/3 csc = -3
cosine = [2sqrt(2)] /3 sec = 3 / [2 sqrt(2)] = [ 3 sqrt(2)] / 4
tangent = [-1] / [2 sqrt(2)] = [- sqrt(2)] / [ 4] cotangent = -2sqrt(2)
4.
sine pi/4 = sqrt2)/2 csc = sqrt(2)
cosine pi/4 = same as sine sec = same as csc
tangent, cotangent pi/4 = 1
5.
sine 2pi/3 = sqrt(3)/2 csc 2pi/3 = 2sqrt(3) / 3
cosine 2pi/3 = -1/2 sec2pi/3 = -2
tangent 2pi/3 = -sqrt(3) cotangent 2pi/3 = -sqrt(3)/ 3
6.
sine180° = 0 csc 180° = undefined
cosine 180° , sec 180° = 1
tangent 180° = 0 cotangent 180° = undefined
