# Parametric Equations

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- Created by: eleanor
- Created on: 19-04-15 11:44

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- Parametric Equations
- Finding the cartesian equation
- Rearrange 1 equation to get t=
- then substitute into the second equation

- use known identities to combine the 2 equations
- rearrange to get sint or cos(t)
- substitue into an equation linking both sin and cos

- rearrange to get sint or cos(t)

- Rearrange 1 equation to get t=
- finding where the curve crosses the axes
- x-axis- y = 0 so set the parametric equation for y equal to 0 and slove for t
- then substitute t into the equation for x to find the point

- x-axis- y = 0 so set the parametric equation for y equal to 0 and slove for t
- finding the value of t at a particular point
- if you have a point a,b then set x(t) = a and y(t)= b and solve to find t

- finding where a parametric curve crosses a straight line
- find the coordinates of the points of interesection of the curve
- substitute the parametric equation into the line
- solve to find t
- substitute t back into the parametric equation

- solve to find t

- substitute the parametric equation into the line

- find the coordinates of the points of interesection of the curve
- Differentiation
- as we have an extra variable t we must use the chain rule
- dy/dx= dy/dt x dt/dx
- remember to flip dx/dt to get dy/dx

- as we have an extra variable t we must use the chain rule
- Integration
- in order to include t the formula is y(dx/dt) dt
- integrate with resoect to t
- differentiate the x-part

- find dx/dt
- rewrite the integral in terms of t
- change the limits into terms of t
- then solve

- change the limits into terms of t

- rewrite the integral in terms of t

- in order to include t the formula is y(dx/dt) dt

- Finding the cartesian equation

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