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

1 Answer

x=22=0.765367 and
y=2+2=1.84776

Explanation:

the x component

x=rcosθ
x=2cos(5π8)

but cos(5π8)=sin(π8)=1cos(π4)2=1122

cos(5π8)=1222

so that

x=2(1222)

x=22=0.765367

the y component

y=rsinθ

y=2sin(5π8)

but sin(5π8)=cos(π8)

cos(π8)=1+cos(π4)2=1+122=122+2

and

y=2(122+2)

y=2+2=1.84776

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