Question

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

Answer 1

Answer:

Part 2:

Based on this evidence,

When b > 1, the period

✔ decreases

.

When 0 < b < 1, the period

✔ increases

Step-by-step explanation:

This is correct for edge 2020. Hope this helps someone.

Answer 2

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 $x = 0$. After completing the rise and fall cycle, the function cuts back to the x axis at $x = 4\pi$.

Then the period $T = 4\pi$.

Second, look at the orange graph when b = 2

Identify a point where the orange chart cuts the x-axis. For example at $x = 0$. After completing the rise and fall cycle, the function cuts back to the x-axis at $x = \pi$.

Then the period $T = \pi$.

We also know that the period of a sinusoidal function is defined as $T(b) = \frac{2\pi}{b}$

So:

$T(0.5) = \frac{2\pi}{0.5} = 4\pi\\\\T(2) = \frac{2\pi}{2} = \pi$