Convert from Polar to Rectangular

Question

Convert the polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation.

r=6cscθ

The rectangular equation for r=6cscθ is ________.

Answer 1

So we have

Answer

The rectangular equation for r = 6 csc θ is y = 6

The graph of r = 6 csc θ is the horizontal line y = 6.

Answer 2

desmos.com/calculator/b7fcygsjnn

Answer 3

r=6cscT = 6/sinT

rsinT= 6= y

y=6 is the line in rectangular coordinates, a flat horizontal line

rcosT = x

r^2= x^2 +y^2

rsinT =y

rcosT= x

T=37 degrees, approximately

cosT=.8

rcosT=8

it's a 10-8-6 right triangle

r^2 = r^2(sin^2(T)) + r^2(cos^2(T)= r^2(sin^2(T) + cos^2(T))= r^2(1)= r^2

play with those identities and find r and x

graph is stretched up by factor of 6 and shifted horizontally by?