value: 7\nmatch the key features of a sine graph to their corresponding values.\nsine graph with a maximum…

Answer:

a. 4. $y = - 1$ b. 3. 3 c. $\frac{1}{2\pi}$ d. 1. $2\pi$

Explanation:

Step1: Find the mid - line

The mid - line of a sine graph is the average of the maximum and minimum values. Let $y_{max}=2$ and $y_{min}=-4$. The mid - line $y=\frac{y_{max} + y_{min}}{2}=\frac{2+( - 4)}{2}=\frac{2 - 4}{2}=-1$.

Step2: Calculate the amplitude

The amplitude $A$ of a sine graph is half the difference between the maximum and minimum values. $A=\frac{y_{max}-y_{min}}{2}=\frac{2-( - 4)}{2}=\frac{2 + 4}{2}=3$.

Step3: Determine the frequency

The period $T$ is given as $2\pi$. The frequency $f$ is the reciprocal of the period, so $f=\frac{1}{T}=\frac{1}{2\pi}$.

Step4: Identify the period

The problem states that the repeating cycle (period) is $2\pi$.