x = 21 cos (pi/8)x=21cos(π8)
y=-21 sin(pi/8)y=−21sin(π8)
pi/8π8 is not an angle for which the value is universally known but you can find it with the trigonometric formula for the bisected angle:
cos(pi/8) = cos (1/2*pi/4) = sqrt(((1+cos(pi/4))/2))= sqrt(((1+sqrt(2))/2)cos(π8)=cos(12⋅π4)=
⎷(1+cos(π4)2)=
⎷(1+√22)
sin(pi/8) = sin (1/2*pi/4) = sqrt(((1-cos(pi/4))/2))= sqrt(((1-sqrt(2))/2)sin(π8)=sin(12⋅π4)=
⎷(1−cos(π4)2)=
⎷(1−√22)
and eventually:
x = 21 sqrt(((1+sqrt(2))/2)x=21
⎷(1+√22)
y=-21sqrt(((1-sqrt(2))/2)y=−21
⎷(1−√22)