Chapter exploration

Parametric equations

Explore

Use the worked example below, then change one input or assumption. Predict which part of the answer must change before calculating.

Explore this related example, then return to the prediction task above.

The point moves with θ. Jump to the special points.

Position along the curve(1.5708, 1.5708)θ = 1.5708

Try an example

Tangent gradient

Normal gradient

vertical

$\theta=\frac\pi2$ : $\frac{dy}{d\theta}=0$ , so the tangent is horizontal.

The tangent is horizontal and the normal is vertical. Both axes use equal scales.

Key idea

For parametric curves, horizontal tangents come from $\frac{dy}{d\theta}=0$ and vertical tangents from $\frac{dx}{d\theta}=0$ .

Ideas to try