In exercise 5.7 and 5.8 you looked and the periodicity and other simple properties of functions. [br]Where,[br][math]y=sin\left(x\right)[/math] has amplitude 1 and period [math]2\pi[/math][br][math]y=cos\left(x\right)[/math] has amplitude 1 and period [math]2\pi[/math][br][math]y=tan\left(x\right)[/math] has no amplitude and period [math]\pi[/math][br][br]In this GeoGebra you are going to look at the different properties and periodicity of each function and what happens when you alter the functions with different functions
[math]y=a\cdot sin\left(bx\right)[/math] has amplitude [math]a[/math] and period [math]\frac{2\pi}{b}[/math][br]Have a play with the GeoGebra below. Start to notice what happens when you move the sliders
Which slider in the GeoGebra changes the amplitude of the function?
Which slider in the GeoGebra changes the period of the function?
Explain what happens to the amplitude of the function f(x) = sin(x) when the amplitude is 5
Explain what happens to the amplitude of the function f(x) = sin(x) when the amplitude is -2.
Explain what happens to the function f(x) = sin(x) when the period (b) is [math]\frac{2\pi}{3}[/math]. (Hence the slider =3)
Explain what happens to the function f(x) when the period(b) is [math]\frac{2\pi}{-1}[/math]. (Hence the slider is -1)