Functions and Locus

The unit circle

You can find the x- and y-coordinate of a point P by using the commands x(P) and y(P)respectively.

• Make a unit circle at the origin.
• Place a point P on the circle and another point with coordinates (1,0).
• Make an angle α from (1,0) to P.
• Make a point A to represent the sine-function, input A=(α,y(P)), the x-coordinate will represent the angle and the y-coordinate will represent the corresponding value of sine.
• Use trace and/or locus to show the trajectory of A as P moves along the circle.
• You can show graph of cosine in a similar way.

Demonstrate derivative and use FormulaText[]

The recording below shows how to demonstrate the derivative in the same way as on the page Calculus - The Definition of the Derivative.

When displaying information about functions, you can use the text tool in the same way as with other objects. There is also a special command

	FormulaText[f]

which will yield the formula of a function as text. This is also shown in the recording below.