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C4 Parametric Differentiation

x=3 cos^2 t y= sin 2t, 0 t < pi

I need to find coordinates of the points where the tangent to the curve is parallel to the x axis. How would i go about doing this?


Is this the stationary point?
therefore dy/dx =0?

However, how would i go about solving this? (really poor i know... it's C2, C3 stuff, i've forgotten...)
Reply 1
Yes, you need to solve dy/dx = 0.

I'm sure that you can find dx/dt and dy/dt. Do you know how to use the chain rule to then find dy/dx?
Reply 2
Original post by Pangol
Yes, you need to solve dy/dx = 0.

I'm sure that you can find dx/dt and dy/dt. Do you know how to use the chain rule to then find dy/dx?


Yeah I've already worked dy/dx using chain rule. It's the next step which i'm struggling with.

dy/dx=0.
therefore -2/3 cot 2t=0.

cos 2t/sin2t=0
so cos 2t=0?

How do i deal with the 2t part (yup really basic maths which i've forgotten, which unit would it be to look up btw? I know how to do cos t, just not cos 2t.)
Reply 3
Original post by Xphoenix
Yeah I've already worked dy/dx using chain rule. It's the next step which i'm struggling with.

dy/dx=0.
therefore -2/3 cot 2t=0.

cos 2t/sin2t=0
so cos 2t=0?

How do i deal with the 2t part (yup really basic maths which i've forgotten, which unit would it be to look up btw? I know how to do cos t, just not cos 2t.)


assuming that's correct up to cos2t = 0 then you're nearly there

2t = arccos0
2t = pi/2
t = pi/4 (and other results)
Reply 4
Original post by Xphoenix
x=3 cos^2 t y= sin 2t, 0 t < pi

I need to find coordinates of the points where the tangent to the curve is parallel to the x axis. How would i go about doing this?


Is this the stationary point?
therefore dy/dx =0?

However, how would i go about solving this? (really poor i know... it's C2, C3 stuff, i've forgotten...)


You don't actually need to find when dy/dx=0, you need to find when dy/dt=0, which will give you the same answer, but you may be unnecessarily finding dx/dt.
Reply 5
Original post by B_9710
You don't actually need to find when dy/dx=0, you need to find when dy/dt=0, which will give you the same answer, but you may be unnecessarily finding dx/dt.


Yeah good point. What i forgot to mention was that they asked you to find dy/dx in the previous part so I knew it had to lead onto the next question and be linked in some way.

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