Question

How do the properties of a Sine Function graph (Amplitude, Period, Domain, Range and X-intercepts) Each relate to the unit circle definition of Sine.

Answer 1

1) Amplitud: in the unit circle, sine is defined as the length of the vertical projection of the (vetical axis) of the point that defines the angle. Whose maximum value is 1, which is the amplitud of the sine function.

2) Period: every complete turn to the circles the angles, and consequently the function sine, repeat. A complete turn is 2π,w hich is the period of the function.

3) Domain: the angle can take any real value,  because you can trace the angles either clock wise or anti-clock wise, and you can do any number of laps.

4) Range: the values of the vertical - intercept (which is what the sine function is) may be between -1 and 1, and that is the range [-1,1].

5) x-intercepts: those are for angles 0, (+/-)π, (+/-)2π, (+/-)3π, (+/-)4π,...

Those are: nπ, with n = +/- 1, +/-2, +/-3, +/-4,...