What are the components of the vector between the origin and the polar coordinate (-2, (5pi)/8)(2,5π8)?

1 Answer

x=sqrt(2-sqrt2)=0.765367x=22=0.765367 and
y=-sqrt(2+sqrt2)=-1.84776y=2+2=1.84776

Explanation:

the x component

x=r cos thetax=rcosθ
x=-2*cos ((5pi)/8)x=2cos(5π8)

but cos ((5pi)/8)=-sin(pi/8)=-sqrt((1-cos(pi/4))/2)=-sqrt((1-1/sqrt2)/2)cos(5π8)=sin(π8)=1cos(π4)2=1122

cos ((5pi)/8)=-1/2sqrt(2-sqrt2)cos(5π8)=1222

so that

x=-2(-1/2sqrt(2-sqrt2))x=2(1222)

x=sqrt(2-sqrt2)=0.765367x=22=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+122=122+2

and

y=-2*(1/2sqrt(2+sqrt2))y=2(122+2)

y=-sqrt(2+sqrt2)=-1.84776y=2+2=1.84776

God bless America ....