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Parametric equtions help

I've been stuck on some parametric questions especially at the start I often get puzzled when asks for various points on the curve. For example in this question I get that theta is 0, but where does that initial 1 come from, and if anything why is it being subbed into the x value and not the y.
p1.PNG36.7KB
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Find dx/dy=0 then solve, since it it a turning point perpendicular to dy/dx
Original post by Owasis
I've been stuck on some parametric questions especially at the start I often get puzzled when asks for various points on the curve. For example in this question I get that theta is 0, but where does that initial 1 come from, and if anything why is it being subbed into the x value and not the y.


Look at the function x=cos⁡(2θ)x=\cos(2\theta). It's just the cosine function. Obviously, it has a maximum of 1. So, x=1x = 1 is the max x-coordinate on the diagram.

Now you want to know what the y coordinate of B is. For that, you need to first solve cos⁡(2θ)=1\cos(2\theta) = 1 for θ\theta, and then substitute it into y=cos⁡θ+2sin⁡θy = \cos \theta + 2\sin \theta.

Nothing puzzling here.

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