the x component
x=r cos thetax=rcosθ
x=-2*cos ((5pi)/8)x=−2⋅cos(5π8)
but cos ((5pi)/8)=-sin(pi/8)=-sqrt((1-cos(pi/4))/2)=-sqrt((1-1/sqrt2)/2)cos(5π8)=−sin(π8)=−√1−cos(π4)2=−√1−1√22
cos ((5pi)/8)=-1/2sqrt(2-sqrt2)cos(5π8)=−12√2−√2
so that
x=-2(-1/2sqrt(2-sqrt2))x=−2(−12√2−√2)
x=sqrt(2-sqrt2)=0.765367x=√2−√2=0.765367
the y component
y=r sin thetay=rsinθ
y=-2 sin ((5pi)/8)y=−2sin(5π8)
but sin ((5pi)/8)=cos (pi/8)sin(5π8)=cos(π8)
cos (pi/8)=sqrt((1+cos(pi/4))/2)=sqrt((1+1/sqrt2)/2)=1/2sqrt(2+sqrt2)cos(π8)=√1+cos(π4)2=√1+1√22=12√2+√2
and
y=-2*(1/2sqrt(2+sqrt2))y=−2⋅(12√2+√2)
y=-sqrt(2+sqrt2)=-1.84776y=−√2+√2=−1.84776
God bless America ....
