1 | initial version |

Plot the curve to gain intuition. Obviously `2*pi`

is a period,
so it is enough to plot the curve for t varying in `[0,2*pi]`

.

```
sage: t = var('t')
sage: parametric_plot((cos(t),cos(2r*t)),(t,0r,2r*float(pi)))
```

To get a formula for `y`

as a function of `x`

, you can use `simplify_trig`

.

```
sage: cos(2*t).simplify_trig()
2*cos(t)^2 - 1
```

Confirm the portion of the parabola indicated by the plot by
observing that `x = cos(t)`

means `x`

varies in `[-1,1]`

.

2 | No.2 Revision |

Plot the curve to gain intuition. Obviously `2*pi`

is a period,
so it is enough to plot the curve for ~~t ~~`t`

varying in `[0,2*pi]`

.

```
sage: t = var('t')
sage: parametric_plot((cos(t),cos(2r*t)),(t,0r,2r*float(pi)))
```

To get a formula for `y`

as a function of `x`

, you can use `simplify_trig`

.

```
sage: cos(2*t).simplify_trig()
2*cos(t)^2 - 1
```

Confirm the portion of the parabola indicated by the plot by
observing that `x = cos(t)`

means `x`

varies in `[-1,1]`

.

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