Parametrics

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Patametric equations

What are parameters, and what are they used for?

Parameters are two equations with variables usually x and y which are related to a third variable usually t. Parameters allow us to compare the two equations forming one single equation which would be known as a Cartesian equation, the Cartesian equation shows us which co-ordinates satisfy both equations.

How do you convert a parametric into a Cartesian equation?

You would do it by finding t of one of the variables and subbing that value of t into the other variable.

For example: x=2t y=2t^2. Cartesian form would be t=x/2, and therefore y=2(x/2)^2.

How do you find out the domain and range?

To find the domain you would have to expand the bounds given in terms of x, For example:

t>12 and x = 2t therefore the range would be 2t>24 and hence x>24

To find the range you would need to find the minimum and/or maximum value of the bounds presented

For example: t>12 and y = t^2 therefore t^2>144 and hence y>144

Conversion between Parametric's and Cartesian equations.

Parametric's are usually presented as x=p(t) and y=q(t), therefore we can combine to two to get a format of y=f(x) in terms of t.

Following this we can therefore say for Cartesian equations that the;

range would be y=q(t) and the domain x=p(t)

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Using trigonometric identities.

How would you draw a curve given 2 trigonometric parametric equations?

List of Trig Functions/Identities

How do you convert trigonemetric equations into Cartesian form?

You would have to know your trigonometric functions to relate the two, For example:

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Curve Sketching

Curve Sketching

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Points of intersection

What should you always attempt when trying to finding the points of intersection?

You should always try to solve for t by substituting the coordinates given, once you have solved for t, once you know t you can proceed to calculate what the question has requested.