Question

Can you please explain what this equation is for and step by step as to how to calculate this question

Answer 1

Answer: The polar equation (r = 2\sin(\theta)) can be converted to Cartesian form using the

relationships between polar and Cartesian coordinates. The conversion involves expressing (r)

and (\sin(\theta)) in terms of (x) and (y). The result is the equation of a circle. The Cartesian

equation equivalent to the polar equation is:

x^2 + (у - 1)^2 = 1

Therefore, the Cartesian form of the polar equation (r = 2\sin(\theta)) is the equation of a circle

with center at ((0, 1)) and radius 1.

Explanation:

Answer 2

Explanation:

Things to recall for polar equations:

y = r sinΦ

x =r cos Φ

and r^2 = x^2 + y^2

r = 2 sin Φ Multiply both sides by 'r'

r^2 = 2 r sin Φ

recall that x^2 + y^2 = r^2

so x^2 + y^2 = 2 r sin Φ but r sin Φ is just 'y' (see above)

so x^2 + y^2 = 2 y re-arrange

x^2 + y^2 - 2y = 0 'complete the square ' for 'y'

x^2 + (y-1)^2 -1 = 0 re-arrange

x^2 + ( y-1)^2 = 1 This is the equation of a circle

with center (h,k) = (0,1) and radius '1'