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# massively confused with C3 differentiation involving radians watch

1. I have an equation of the curve 'x = 2siny'

I have to show that 'dy/dx = 1/square root of 2' at point 'p' on the curve

point 'p' is: (square root of 2, pi/4)

The equation has 'x =...' instead of the usual 'y=....', so how do I differentiate 'x = 2siny'.

after I differentiated it, do I sub in the 'x' or 'y' co-ordinates of point 'p' into it ???

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I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
2. You've got the equation x=2siny.

Find dx/dy (instead of dy/dx), because you can do this like you would normally (in other words, pretend x is y and y is x in the equation above.

Then use the fact that dy/dx = 1 / (dx/dy).

Then evaluate your expression for dy/dx at y=pi/4 (the y coordinate of the point p).
3. (Original post by Drederick Tatum)
You've got the equation x=2siny.

Find dx/dy (instead of dy/dx), because you can do this like you would normally (in other words, pretend x is y and y is x in the equation above.

Then use the fact that dy/dx = 1 / (dx/dy).

Then evaluate your expression for dy/dx at y=pi/4 (the y coordinate of the point p).

so, once I have diferentiated the equation like I would normally do with x's, I just put it below '1' in a fraction?

btw I never knew dy/dx = 1 / (dx/dy)
4. What about the 2nd question?

I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
5. (Original post by PRudd)

I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
yeah, I know I could use 'dx/dy' for the equation 'x = cos(2y+pi). But I am not sure how to differentiate 'pi'.
6. pi is just a constant between 3 and 4. So d/dx(pi) = 0
7. (Original post by Drederick Tatum)
pi is just a constant between 3 and 4. So d/dx(pi) = 0
But can cos(2y+pi) be split when differentiating?
8. (Original post by W.H.T)
...I have another question which asks me to find the equation of the tangent to the curve 'x = cos(2y+pi)' at (0,pi/4). I know I have to first differentiate the equation, but just have no idea how to do it when its 'x=....'
I know whats going on now

dx/dy = -2Sin(2y + Pi)

Put in value of y. This gives dx/dy = 2

This means that dy/dx =0.5 and then you can use y-y1 = m(x-x1) to get the final equation.

Phew... I can sleep happy

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