connecting the graph of the sine function to the unit circle. directions: at each arrow: a. plot the…

Answer:

Question 1:

For $t = \frac{\pi}{2}$, the coordinates of the terminal - point are $(x,y)=(0,1)$. The value of the $\sin(t)$ function is $1$.

Question 2:

B3

Explanation:

Step1: Recall unit - circle and sine function

The sine of an angle $t$ in the unit - circle is defined as the $y$ - coordinate of the terminal point on the unit circle corresponding to the angle $t$. When $t=\frac{\pi}{2}$, on the unit circle, the terminal point is $(0,1)$, so $\sin(\frac{\pi}{2}) = 1$.

Step2: Analyze periodicity of sine function

The sine function $y = \sin(t)$ has a period of $2\pi$. The graph of $y=\sin(t)$ is symmetric and repeats every $2\pi$. For a sine - wave graph related to the unit circle, if we consider the points on the graph and their corresponding terminal points on the unit circle, the point with the same coordinates as $A2$ will be a full - period or half - period (in some symmetric cases) away. In the context of the sine function's graph and unit - circle connection, the point that has the same coordinates as $A2$ is $B3$.