108k views
2 votes
Convert (xy)^2=9 to an equation in polar coordinates [answer]=r^18

Convert (xy)^2=9 to an equation in polar coordinates [answer]=r^18-example-1
User Ino
by
8.2k points

1 Answer

1 vote

In polar coordinates,
r^18 = 2^9.

Polar coordinates: We convert x and y to r and t using x = r cos(t) and y = r sin(t).

Substitute: Replace xy with
r^2 sin(t) cos(t) in the given equation.

Simplify: Raise both sides to the power of 9 and expand using DeMoivre's Theorem:
(r^2 sin(t) cos(t))^9 = 2^9. This simplifies to
r^18 sin(18t) cos(18t) = 2^9.

Magnitude: Since the magnitude (r) doesn't depend on the angle (t), we can isolate it by taking the absolute value of both sides. This leads to
|r^18| = 2^9.

Therefore,
r^18 = 2^9

User Punita
by
9.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories