Answer to Question #271766 in Analytic Geometry for Bebe

Question

1.Convert the polar coordinates (-8, ) into rectangular coordinates.

2.Convert the rectangular coordinates (3, -3) into polar coordinates with r > 0 and 0 ≤ θ < 2π.

3.Convert the rectangular equation x2 + y2 = 100 into a polar equation that expresses r in terms of θ.

4.Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in terms of x.

Answer 1

$x=rcos\theta,y=rsin\theta$

1.:

$x=8cos\theta,y=8sin\theta$

2.

$3=rcos\theta,-3=rsin\theta$

$tan\theta=-1$

since $x>0,y<0$

$\theta=7\pi/4$

$r=3/cos(7\pi/4)=3\sqrt 2$

3.

$(rcos\theta)^2+(rsin\theta)^2=100$

$r^2=100$

$r=10$

4.

$4x+y=8$

$y=8-4x$