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

1 Answer
Leland Adriano Alejandro
Feb 12, 2016

x=√2−√2=0.765367 and
y=−√2+√2=−1.84776

Explanation:

the x component

x=rcosθ
x=−2⋅cos(5π8)

but cos(5π8)=−sin(π8)=−√1−cos(π4)2=−√1−1√22

cos(5π8)=−12√2−√2

so that

x=−2(−12√2−√2)

x=√2−√2=0.765367

the y component

y=rsinθ

y=−2sin(5π8)

but sin(5π8)=cos(π8)

cos(π8)=√1+cos(π4)2=√1+1√22=12√2+√2

and

y=−2⋅(12√2+√2)

y=−√2+√2=−1.84776

God bless America ....

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