Combining 2 Equations into 1 Polar Equation

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To combine the two given equations into one polar equation, start by squaring both equations: x(θ) = a*cos(θ)*sin(k*θ) and y(θ) = a*sin(θ)*sin(k*θ). Then, add the squared equations together using the formula r² = x² + y². This approach allows for the derivation of a single polar equation that represents the relationship between r, θ, and the constants a and k. Following this method will yield a unified polar representation of the original equations.
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If I have 2 equations as shown below, how can I make them into 1 polar equation?

x(theta) = a*cos(theta) * sin(k*theta)
y(theta) = a * sin(theta) * sin(k*theta)

Thanks very much
 
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r = radius from x and y:

r^2 = x^2 + y^2
 
To maybe add a little to out's hint, square both of the equations you have and add them together. See what happens :).
 

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