Eliminate the parameter to express the following parametric equations as a single equation in x and y. x=2\sin 8t, y=2\cos 8t

generals336

generals336

Answered question

2021-02-26

Eliminate the parameter to express the following parametric equations as a single equation in x and y.
x=2sin8t,y=2cos8t

Answer & Explanation

nitruraviX

nitruraviX

Skilled2021-02-28Added 101 answers

Step 1
We have 2 parametric equations
The given equations are:
x=2sin8t,y=2cos8t
We have to eliminate the parameter to express the following parametric equations as a single equation in x and y.
Step 2
We have,
x=2sin8t,y=2cos8t
x2=sin8t,y2=cos8t
(x2)2+(y2)2=sin28t+cos28t=1
Hence, the parametric equations as a single equation in x and y is
Answer: (x2)2+(y2)2=1

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