133k views
3 votes
x= cos 2 t, y=sin 2 t A pair of parametric equations is given. Sketch the curve represented by the parametric equations.

1 Answer

4 votes

Final answer:

The curve represented by the parametric equations x = cos 2t and y = sin 2t is a circle with radius 1 centered at the origin.

Step-by-step explanation:

To sketch the curve represented by the parametric equations x = cos 2t and y = sin 2t, we can use the trigonometric identities to express x and y in terms of each other. Since cos^2(x) + sin^2(x) = 1, we can rewrite x = cos 2t as x^2 + y^2 = 1. This represents a circle with radius 1 centered at the origin. Therefore, the curve represented by the parametric equations is a circle.

At any given t, the coordinates (x, y) on the circle correspond to a point on the curve. We can plot several points on the circle by substituting different values of t into the equations. Connecting these points will give us a complete sketch of the curve.

User Boyan
by
8.5k points