Chapter 6.4, Problem 105AYU

To determine

What is the relation between the angle and the $y-coordinate$ of point $C$ .

Answer to Problem 105AYU

  $\boxed{SineWave}$

Explanation of Solution

Given information:

On the screen you will see the graph of the unit circle with point $C$ labelled. Use your mouse and move point $C$ around the unit circle in the counter-clockwise direction. What do you notice? In particular, what is the relation between the angle and the $y-coordinate$ of point $C$ .

Calculation:

Consider the graph,

  

A graph of unit circle on the screen of the trace sine curve applet having a point $C$ on its circumference, moving anticlockwise making an angle with the positive direction of $x-axis$ .

The height of the point $C$ is known as sine of angle determined by that point from the center of circle.

As the point $C$ is dragged the angle sin $C$ also varies.

Now as point $C$ moves around its circle while moving time along its axis simultaneously, point P leaves behind a trace of where it has been.

Hence, the resulting curve is a sine wave. Point $C$ moving around unit circle as a function of time.