Press the play button or move the slider.
What is the x-value of the red point?
What is the y-value of the red point?
Tracing the red points results in the graph of [math]y=sin\left(\theta\right)[/math].[br]This sine function relates an angle measure in radians to the y-value of a point on the unit circle.
What type of function is the sine function?
How does changing the slider for [i]a[/i] affect the graph of this sine function?
What happens to the graph when [i]a[/i] is negative?
How does changing the slider for [i]b[/i] affect the graph of this sine function?
For the periodic function [math]y=a\cdot sin\left(b\theta\right)[/math], where [math]a\ne0[/math], [math]b>0[/math], and [math]\theta[/math] is an angle in radians:[br][list][*]The amplitude of the function is [math]|a|[/math].[/*][*]The function has [math]b[/math] cycles between 0 and [math]2\pi[/math].[/*][*]The period of the function is [math]\frac{2\pi}{b}[/math].[br][/*][/list]
Which function would have an amplitude of 4?
Which function would have a period of pi?
[list=1][*]Draw an x-axis from 0 to the period of the function. Divide the period into 4 pieces.[/*][*]Draw a y-axis from the amplitude to the opposite of the amplitude.[/*][*]Use a five-point summary to sketch the graph of a sine function:[i] [/i][/*][/list][i] zero-max-zero-min-zero[/i] if [i]a[/i] is positive.[br][i]  zero-min-zero-max-zero[/i] if [i]a[/i] is negative.
Sketch the graph of [math]y=\frac{1}{2}sin\left(2\theta\right)[/math].
Write an equation for the sine function shown above.
pg. 848 - 849[br]#15 - 30 all, 47, [br]48