LFS with idea for parametric function by R.B. Lane, idea for pseudo-slider by Zen Biker Maniac.
Created with GeoGebra
a.You know the standard formula for the unit circle x2+y2=1.
Look at the parametric function for the unit circle.
The parameter is θ.
The x-value is cos(θ) and the y-value is sin(θ).
These are the coordinates of the point P.
b. Click and drag the green point on the slider for θ from 0° to 360° (bottom right).
Watch the point P go around the circle.
On this graph we can "see" the parameter as the angle.
1. Pick an angle between 0° and 360°.
• Type in the value of the angle you picked (no degree sign!)
• Then click on the Set Angle button.
2. Using a calculator, find x and y.
• Find cosine of this angle. Write this value down as x=....
• Now find sine of this angle. Write this value down as y=...
• Let's check. Click on Show cos(θ) and Show sin(θ).
3. Using these values, calculate x2+y2. It should be 1.
• Click on Show Calculation.
4. This means the point (x,y) is on the unit circle. Why?
• Find the point P on the unit circle.
• Let's check. Click on Show P.
• Click on Reset to start over.
LFS with idea for parametric function by R.B. Lane, idea for pseudo-slider by Zen Biker Maniac.
Created with GeoGebra