Trigonometric Functions of Real Numbers

This applet illustrates the definitions of the trigonometric functions with real arguments between [math]0[/math] and [math] 2 \pi[/math]. Let [math]0< t < 2 \pi [/math] and let the point [math]P(x,y)[/math] be the point on the unit circle corresponding to [math]t[/math]. Then [math]x=cos(t)[/math] and [math]y= sin(t)[/math]. Enter [math]x(P) [/math]for the [math]x[/math] coordinate of [math]P[/math] and [math]y(P) [/math]for the [math]y[/math] coordinate of [math]P[/math]. For example, for the definition of [math] tan(t) = \frac{y}{x}[/math] we will enter [math]y(P)/x(P)[/math] in the input box for [math]f(t)[/math]. The applet traces the point [math]F(t, f(t))[/math] as we drag point [math]P[/math] along the unit circle or animate it.