graph the function $y = \\frac{1}{2} \\sin(2x)$. click and drag the highlighted points to shift the graph…

Explanation:

Step1: Identify the amplitude

The amplitude $A$ is the coefficient of the sine function. $$A = \frac{1}{2} = 0.5$$

Step2: Calculate the period

The period $P$ is calculated using the coefficient of $x$, which is $2$. $$P = \frac{360^{\circ}}{2} = 180^{\circ}$$

Step3: Determine key points

The graph starts at $(0,0)$, reaches a maximum at $\frac{P}{4}$, and returns to zero at $\frac{P}{2}$. $$\text{Max point: } (\frac{180^{\circ}}{4}, 0.5) = (45^{\circ}, 0.5)$$ $$\text{Intercept: } (\frac{180^{\circ}}{2}, 0) = (90^{\circ}, 0)$$

Answer:

To graph $y = \frac{1}{2} \sin(2x)$, set the amplitude to $0.5$ and the period to $180^{\circ}$. The blue point should be at $(0,0)$, the yellow maximum point at $(45^{\circ}, 0.5)$, and the red point (end of one cycle) at $(180^{\circ}, 0)$.