convert polar equations to rectangular coordinates.

Question

1.) θ=π

2.) r=6 cos θ

3.) sec θ=2

Answer 1

x=r*cos(è)
y=r*sin(è)

1.)

x=r*cos(è)=r*cos(ð)=r*(-1)= -r

y=r*sin(è)=r*sin(ð)=r*0=0

2.)

x=r*cos(è)=6*cos(è)*cos(è)=6*cos(è)^2

y=r*sin(è)=6*sin(è)*cos(è)=6*(1/2)*sin(2è)=3*sin(2è)

3.)

sec(è)=2

sec(è)=1/cos(è)=2

cos(è)=1/2

sin(è)=sqroot(1-cos(è)^2)

sin(è)=sqroot(1-(1/2)^2)

sin(è)=sqroot(1-1/4)

sin(è)=sqroot(3/4)

sin(è)=sqroot(3)/2

x=r*cos(è)=r/2

y=r*sin(è)=r*sqroot(3)/2

Answer 2

1)y=0, x<0 (the ray)
2)r^2=6r*cos(teta)
x^2+y^2=6x
x^2-6x+9-9+y^2=0
(x-3)^2+y^2=3^2 (the circle)
3)2cos(teta)=1
2r*cos(teta)=r
2x=sqrt(x^2+y^2) (x>0)
4x^2=x^2+y^2
y^2=3x^2
y=(+-)sqrt(3)x (two rays)