Starter challenge Parametric equations Cartesian equations KUS objectives
Starter: challenge
Parametric equations: Cartesian equations KUS objectives BAT convert between parametric and Cartesian equations of a function Starter: previous page Geogebra: parametric eqns http: //ggbtu. be/mni 1 QRU 41
WB 5 Parametric eqns – cartesian eqn example I Find the Cartesian equations of the following curves
WB 6 find the Cartesian equations of these (eliminate the parameters) answers i) iii) iv) v) vi)
t -3 -2 -1 0 1 2 3 x = 1/(t+1) -1/2 -1 1 ½ 1/3 ¼ y = t 2 9 4 1 0 1 4 9 Hmmmm… is this enough to sketch this graph? …… NO! Cartesian equation of the curve? This has a horizontal asymptote at y=1 and a vertical asymptote at x=0
WB 8 Trigonometric Parametric eqns – cartesian eqn Look back at WB 3 a this is a unit circle centre (0, 0)
A Cartesian equation is just an equation of a line where the variables used are x and y only How can we link sin t and cos t in an equation? The equation is that of a circle Think about where the centre will be, and its radius 5 Centre = (2, -3) Radius = 1 -5 5 -5
double angle formula Replace sint with x b) Geogebra: parametric eqns Replace sin 2 t with x 2 We can now replace cos t Another way of writing this (by squaring the whole of each side) http: //ggbtu. be/mni 1 QRU 41
WB 11 find the Cartesian equations of these (eliminate the parameters)
WB 11 find the Cartesian equations of these (eliminate the parameters) First find a link Now find an expression for sin t think of simultaneous equations
WB 11 find the Cartesian equations of these (eliminate the parameters) First find a link
WB 11 find the Cartesian equations of these (eliminate the parameters) Addition formula
Parametric equations –Summary Parametric equations are written as: four main types of question • Sketch a graph from parametric equations • Eliminate (t) to find the Cartesian equation • Differentiating to find gradients, tangents and normal • Integrating to find area under a graph Write one thing you have learned Write one thing you need to improve A Cartesian equation would be
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