SOLUTION: Write the following polar equations in Cartesian form. a) {{{r^2}}}= 7 b) θ = 4pi/3 c) θ = 7pi/4 d) r = cosθ

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Write the following polar equations in Cartesian form. a) {{{r^2}}}= 7 b) θ = 4pi/3 c) θ = 7pi/4 d) r = cosθ       Log On


   

Question 1157772: Write the following polar equations in Cartesian form.
a) r%5E2= 7
b) θ = 4pi/3
c) θ = 7pi/4
d) r = cosθ
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a)
r%5E2=+7
using the formulae that link Polar to Cartesian coordinates:
r%5E2=x%5E2%2By%5E2
x%5E2%2By%5E2=7-> rectangular form

b)
theta=+4pi%2F3
Take the tangent of both sides:
tan%28theta%29=+tan%284pi%2F3%29

Substitute tan%28theta%29=y%2Fx
y%2Fx=+tan%284pi%2F3%29
Multiply both sides by x:
y=+tan%284pi%2F3%29%2Ax

Substitute tan%284pi%2F3%29=sqrt%283%29

y=sqrt%283%29%2Ax-> rectangular form


c)
theta+=+7pi%2F4
tan%28theta%29+=+tan%287pi%2F4%29
y%2Fx=+tan%287pi%2F4%29
y%2Fx=+-1
y=+-x-> rectangular form

d)
r+=+cos%28theta%29
using the formulae that link Polar to Cartesian coordinates:
r%5E2=x%5E2%2By%5E2
x=r%2Acos%28theta%29+and y=r%2Asin%28theta%29
for this question given : r=cos%28theta%29 => r=x%2Fr
multiply both sides by r: => r%2Ar=xr%2Fr => r%5E2=x
=> x%5E2%2By%5E2=x-> rectangular form