A Trigonometric Problem

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