Parametric equations differentiation KUS objectives BAT Find the

Parametric equations: differentiation KUS objectives BAT Find the gradient from parametric equations – solve problems with tangents and normals Find the point on the curve y = f(x) when t = -1 Find the Cartesian equation y = f(x) from the parametric equations Find the Area under the curve y = f(x) between t = -1 and t = 1 Geogebra: parametric eqns http: //ggbtu. be/mni 1 QRU 41

Notes gradient function When a curve is given in parametric equations: • Differentiate y and x with respect to the parameter t • We can then use the following version of the chain rule

find the gradient at point P by differentiating and substituting θ in Find the coordinates of x and y at point P The coordinates of P are: Use the formula y – y 1 = m(x – x 1) to obtain the equation of the line

Find the value of t find the gradient at the point by differentiating and substituting θ in Use the formula y – y 1 = m(x – x 1) to obtain the equation of the line

find the gradient at point P by differentiating and substituting θ in find the gradient of the normal Gradient of the normal at P: Find the coordinates of x and y at point P The coordinates of P are: Use the formula y – y 1 = m(x – x 1) to obtain the equation of the line

find the gradient at point P by differentiating and substituting θ in find the gradient of the normal Gradient of the normal at P: Find the coordinates of x and y at point P The coordinates of P are: Use the formula y – y 1 = m(x – x 1) to obtain the equation of the line

Exercise: try the five questions in the workbook

Crucial points 1. It can help to sketch any curve first on a graphing programme 2. Make sure that you are able to differentiate functions involving sine and cosine confidently 3. You need to be able to use the chain rule This will help you find the gradient of a curve at a particular point. You can then use it to identify any turning points or find the gradient of the normal. You may find it helpful to use it in this form: 4. Remember the relationship between the gradients of a tangent and a normal

BAT draw graphs from parametric equations • BAT convert between parametric and cartesian equations • BAT find gradient from parametric equations Parametric equations are written as: A Cartesian equation would be There are three types of question in the exam • Sketch a graph from parametric equations • Eliminate (t) to find the Cartesian equation • Differentiating to find gradients, tangents and normals Revise Substitution to find point (x, y) Perpendicular gradients; formula for equation of a line Parametric eqns –Summary

You should be able to: BAT Find the gradient from parametric equations – solve problems with tangents and normals Write one thing you have learned Write one thing you need to improve

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