Codebymath.com - Online coding lessons using rotate a parabola

Lesson goal: For loops and rotating math functions for plotting

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In a previous lesson you plotted a parabola. Plotting something like

$y=x^2$ might seem pretty easy. But what if you wanted to draw a parabola that was rotated by say

$15^\circ$ ? How would you do that?

It turns out that if you want to rotate an

$(x,y)$ point through an angle of

$\theta$ , you can use these equations to compute a new

$(x,y)$ pair, that is rotated through and angle

$\theta$ :

$xp = x \cos\theta - y \sin\theta$

$yp = x \sin\theta + y \cos\theta$

In this notation, if

$x$ and

$y$ are your unrotated (or "normal") points, then

$xp$ and

$yp$ will be where the point would be, if rotated through

$\theta$ degrees.

Now you try. Program in the rotation formulas above and see if you can draw a parabola rotated through $15^\circ$ .

Type your code here:

 
pcls(0)
theta = ??
for x=-100,100 do
  y = 0.1*x^2
  xp = ??
  yp = ??
  pset(xp,yp)
end

See your results here:

You can use dcos(..) and dsin(..) for sin and cos functions that use degrees, or math.cos(..) and math.sin(..) for functions that use radians.

When done rotating a parabola, trying rotating a sine-wave, or a line, a $x^4$ polynomial, or any other math function you want!

Lesson goal: For loops and rotating math functions for plotting

Now you try. Program in the rotation formulas above and see if you can draw a parabola rotated through 15∘15^\circ.

Share your code

Now you try. Program in the rotation formulas above and see if you can draw a parabola rotated through $15^\circ$ .