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Match equation graph with its parametric equation Not all equations will be used_ All graphs shown for 5 < t< 5

x(t) = +2 y(t) = + z(t) = et y(t) = + x(t) = t + cos(t) y(t) = t + sin(t) 2(t) = + _ t y(t) =+

3 ] 3–

x(t) = + y(t) = +

5 – < –

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04:54

Match the parametric equations with the graphs labeledI-VI. Give reasons for your choices. (Do not use a graphing device.)(a) $x=t^{4}-t+1, \quad y=t^{2}$(b) $x=t^{2}-2 t, \quad y=\sqrt{t}$(b) $x=t^{2}-2 t, \quad y=\sin (t+\sin 2 t)$(d) $x=\cos 5 t, \quad y=\sin 2 t$(d) $x=\cos 5 t, \quad y=t^{2}+\cos 3 t$(e) $x=\frac{\sin 2 t}{4+t^{2}}, \quad y=\frac{\cos 2 t}{4+t^{2}}$

01:28

Match the parametric equations with the graphs labeled I-VI.Give reasons for your choices. (Do not use a graphing device.)$$\begin{array}{l}{\text { (a) } x=t^{4}-t+1, \quad y=t^{2}} \\ {\text { (b) } x=t^{2}-2 t, \quad y=\sqrt{t}} \\ {\text { (c) } x=\sin 2 t, \quad y=\sin (t+\sin 2 t)} \\ {\text { (d) } x=\cos 5 t, \quad y=\sin 2 t} \\ {\text { (e) } x=t+\sin 4 t, \quad y=t^{2}+\cos 3 t} \\ {\text { (f) } x=\frac{\sin 2 t}{4+t^{2}}, \quad y=\frac{\cos 2 t}{4+t^{2}}}\end{array}$$

01:16

Match the parametric equations with the graphs labeled I-VI. Give reasons for your choices. (Do not use a graphing device.)(a) $x=t^{4}-t+1, \quad y=t^{2}$(b) $x=t^{2}-2 t, \quad y=\sqrt{t}$(c) $x=\sin 2 t, \quad y=\sin (t+\sin 2 t)$(d) $x=\cos 5 t, \quad y=\sin 2 t$(e) $x=t+\sin 4 t, \quad y=t^{2}+\cos 3 t$(f) $x=\frac{\sin 2 t}{4+t^{2}}, \quad y=\frac{\cos 2 t}{4+t^{2}}$

01:11

Graphs of Parametric Equations Use a graphing device to draw the curve represented by the parametric equations.$$x=3 \sin 5 t, \quad y=5 \cos 3 t$$

02:35

Graphs of Parametric Equations Match the parametric equations with the graphs labeled I-IV. Give reasons for your answers.$$x=t+\sin 2 t, \quad y=t+\sin 3 t$$

Transcript

Okay, so let’s get started with the first graph here. The important feeling is that, on the left hand, side of our cartesian plane, the coordinate, is negative, so in particular we can notice that we can walk, because the y coordinate is always positive. The same thing that is it work because the y coordinate is positive and the same thing. So at this point we just need to choose between this 1 and this 1 here, okay! Well, what is the right? 1 here? Okay, we’re going to have that this! The .10 belongs to this cue, okay, so…

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