Parametric functions

WB1 A curve is defined by the parametric equations x=2 t−1 y=3 t2 a) Write down the Cartesian coordinates of the point where t = -2b) What is the value of t at the point with Cartesian coordinates (5, 27) ?C) sketch the graphs of x-t, y-t and y-x

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Parametric functions

WB2 Draw/sketch the curves on x and y axes given by the Parametric Equations

a¿ x=2 t y=t2 for −3≤ t ≤3

b¿ x=t+2 y=1t for −3≤ t ≤3

c ¿ x=t2 y=t3−t for −3≤ t ≤3

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Parametric functions WB3 Draw the curves given by the following Parametric Equations, in the range −π ≤t ≤ π

a) x=sin t y=cos t

b¿ x=sin t y=1+cos t

c ¿ x=1+cos t y=sin t

d ¿ x=4 cos t y=4sin t

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Parametric functions

Challenge create each picture using parametric functions

Equations:

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Parametric functions

WB4 Other curvesDraw the curves given by the following Parametric Equations, in the range −π ≤t ≤ π

a¿ x=2 s∈t y=3cos t

b¿ x=sin 2 t y=4sin t

c ¿ x=1−cos t y=2sin 2 t

d ¿ x=cos2 t y=2sin t

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Parametric functions

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Parametric functions

Cartesian equations

WB5 Find the Cartesian equations of the following curves

a) x=t−1 y=2t 2+3t t∈ R

b) x=t 2 y=2t 2+3t t ≥0

WB6 Find the Cartesian equations of the following curves

i) x=4 t , y=3−t

ii) x=t−1 , y=t 2+1

iii) x=2 t2 , y=4 (t−1)

iv) x=t+2 , y=1t

v) x=t 2−1 , y=t 2+1

vi) x=t 2−1 , y=t4+1

WB7 Evil question

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Parametric functions Draw the curve given by the Parametric Equations

x= 1t+1 y=t2 for −3≤ t ≤3

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Parametric functions

Cartesian equations and Trigonometry

Try to rearrange the parametric equations to get sin t=… and cos t=… Then use the identity sin2 t+cos2 t=1 If this does not work you may need to rearrange a different way – look for a connection

between the parametric equations or an Identity you could use

WB8 Find the Cartesian equation of the following curvex=sin t y=cos t for -π ≤t ≤ π

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Parametric functions

WB9 A curve has Parametric equations: x=sint+2 y=cost−3a) Find the Cartesian equation of the curveb) Sketch the curve

WB10 A curve has Parametric equations: x=sint y=sin2 ta) Find the Cartesian equation of the curveb) Sketch the curve

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Parametric functions WB11 find the Cartesian equations of these (eliminate the parameters using a suitable identity)

a¿ x=3sin t , y=2cos t

b¿ x=1+cos t , y=1−2 sint

c ¿ x=cos t+sin t, y=2cos t+sin t

WB11 find the Cartesian equations of these (eliminate the parameters using a suitable identity)

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Parametric functions

d ¿ x=sec t , y=5 tan t

e ¿x=2cos t−1, y=3+2sin t

f ¿ x=cos(t+ π4 ) , y=√2sin t

Problem solving

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Parametric functions WB12 The diagram shows a sketch of the curve with Parametric equations: x=t−1

y=4−t 2

The curve meets the x-axis at the points A and B. Find their coordinates.

WB13 A curve has Parametric equations: x=at y=a(t 3+8)Where a is a constant. Given that the curve passes through (2,0), find the value of a

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Parametric functions

WB14 A curve has Parametric equations: x=t 2 y=4 tThe line x + y + 4 = 0 meets the curve at point A. Find the coordinates of A.

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