Unit Circle - Parametric Function

1. Draw the unit circle

a.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.

2. Understand the unit circle.

a. Pick an angle between 0° and 360°.

• Type in the value of the angle you picked below (without °).
• Then click on the Set Angle button.

b. Using a calculator, find the coordinates of P, as follows.

• Put your calculator in degree mode.

• 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).

c. Using these values, calculate x²+y². It should be 1.

d. This equation implies that (x,y) is on the unit circle. Why?

• Find the point P on the unit circle.

Move the slider for θ and see how the equations change.