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Jurrasic
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Is it right to multiply everything on both sides first, by the (2-sin^2 θ) ? Why would you want to do that? In terms of how it should look, and what variable to solve for, what exactly is the goal here and why?
You don't necessarily solve for a variable. The goal is to rewrite the equation so that the variables are x's and y's, not r's and θ's. After multiplying both sides by the denominator, add sin2 θ to both sides, and then use the equations that vela gave you. (They are the same one's I mentioned in your previous thread.)Jurrasic said:In terms of how it should look, and what variable to solve for, what exactly is the goal here and why?
The equation for R^2 is 8/(2-sin^2 θ).
R^2 can be converted to rectangular form by using the double angle formula for sine, which is sin^2 θ = (1-cos2θ)/2. Substituting this into the equation for R^2 gives us 8/(2-(1-cos2θ)/2) = 16/(4-cos2θ).
Yes, R^2 can be simplified further by using the Pythagorean identity for cosine, which is cos2θ = 1-2sin^2 θ. Substituting this into the equation for R^2 gives us 16/(4-(1-2sin^2 θ)) = 16/(3+2sin^2 θ).
To graph R^2 in rectangular form, we can plot points by choosing different values for θ and calculating the corresponding values for R^2 using the simplified equation, 16/(3+2sin^2 θ). This will give us a curve that can be plotted on a graph.
The range of values for R^2 in rectangular form is all real numbers except for when sin^2 θ = -3/2. This is because the denominator of the simplified equation, 3+2sin^2 θ, cannot equal 0. Therefore, the range of values for R^2 is (-∞, ∞) excluding -3/2.