When b= 0.5, the period of orange graph is _ piWhen b= 2, the period of orange graph is _ pi

Answer:When b= 0.5, the period of orange graph is _4_ pi When b= 2, the period of orange graph is _1_piStep-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]