1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates. 1b) Use a trigonometric identity to show that the polar equation can be simplified as r^2 = 2 cos 2θ. Explain why all the solutions of the original equation are still solutions of this equation (noting that you have probably divided both sides by r^2).

1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates. 1b) Use a trigonometric identity to show that the polar equation can be simplified as r^2 = 2 cos 2θ. Explain why all the solutions of the original equation are still solutions of this equation (noting that you have probably divided both sides by r^2).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.6: Polar Equations Of Conics

Problem 29E

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Question

Please answer the following equations with full working out

1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates.
1b) Use a trigonometric identity to show that the polar equation can be simplified
as r^2 = 2 cos 2θ. Explain why all the solutions of the original equation are still
solutions of this equation (noting that you have probably divided both sides by
r^2).

Equations that give the relation between different trigonometric functions and are true for any value of the variable for the domain. There are six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

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