Answer:
When b= 0.5, the period of orange graph is _4_ pi
When b= 2, the period of orange graph is _1_pi
Step-by-step explanation:
The period of the sinusoidal functions can be easily calculated by observing their graphs.
First, look at the orange graph when b = 0.5
Identify a point where the orange chart cuts the x-axis. For example at [tex]x = 0[/tex]. After completing the rise and fall cycle, the function cuts back to the x axis at [tex]x = 4\pi[/tex].
Then the period [tex]T = 4\pi[/tex].
Second, look at the orange graph when b = 2
Identify a point where the orange chart cuts the x-axis. For example at [tex]x = 0[/tex]. After completing the rise and fall cycle, the function cuts back to the x-axis at [tex]x = \pi[/tex].
Then the period [tex]T = \pi[/tex].
We also know that the period of a sinusoidal function is defined as [tex]T(b) = \frac{2\pi}{b}[/tex]
So:
[tex]T(0.5) = \frac{2\pi}{0.5} = 4\pi\\\\T(2) = \frac{2\pi}{2} = \pi[/tex]
