Question

based on your results from the prev plot the graph of v = sin(θ). note that you must define two points to create the graph. there are two options for the points you must provide. option one is to pick one of the points with a minimum function output value and one point with a maximum function output value. option two is to pick one point along the functions midline and one point with a maximum function output value.

Explanation:

Step1: Find the maximum value of \( y = \sin(\theta) \)

The range of the sine function \( y=\sin(\theta) \) is \( y\in[- 1,1] \). The maximum value of \( y = \sin(\theta) \) occurs when \( \theta=\frac{\pi}{2}+2k\pi,k\in\mathbb{Z} \). For simplicity, we can take \( \theta=\frac{\pi}{2} \), and \( y = \sin(\frac{\pi}{2})=1 \).

Step2: Find a non - maximum value (mid - line or minimum)

The mid - line of \( y=\sin(\theta) \) is \( y = 0 \). When \( \theta = 0 \), \( y=\sin(0)=0 \). (Alternatively, if we consider the minimum value, when \( \theta=\frac{3\pi}{2}+2k\pi,k\in\mathbb{Z} \), for simplicity \( \theta=\frac{3\pi}{2} \), \( y=\sin(\frac{3\pi}{2})=-1 \))

Answer:

Plot the point \((\frac{\pi}{2},1)\) (maximum point) and \((0,0)\) (mid - line point) (or \((\frac{3\pi}{2}, - 1)\) (minimum point) and \((\frac{\pi}{2},1)\)) on the given coordinate system to draw the graph of \(y = \sin(\theta)\)