Question

Transform the following polar equation into an equation in rectangular coordinates r = 4

PLS HELP ty

Answer 1

The rectangular equation equivalent to the polar equation r = 4 is x^2 + y^2 = 16.

Explanation:

The polar equation r = 4 can be transformed into an equation in rectangular coordinates by using the following relationships between polar and rectangular coordinates:

x = r cos(theta)

y = r sin(theta)

Substituting r = 4 into these equations, we get:

x = 4 cos(theta)

y = 4 sin(theta)

Therefore, the rectangular equation equivalent to the polar equation r = 4 is:

x^2 + y^2 = (4 cos(theta))^2 + (4 sin(theta))^2 = 16(cos^2(theta) + sin^2(theta)) = 16