Chapter 13.2, Problem 3OE

To determine

To find: The value of $\sin s$ is between a $-1$ and $1$ , and sketch a circle.

Answer to Problem 3OE

The value of $\sin s$ is between $-1$ and $1$ because the range of the unit circle is from $-1$ to $1$ , and sketch of the circle is shown in figure $\left(1\right)$ .

Explanation of Solution

Given information:

The given equation is

  $x^2+y^2=1$

To graph:

Using MAPLE to graph the given expression.

  $$

Figure $\left(1\right)$

Clearly, from the graph $\sin s$ represents the projection of the radius onto the $y-axis$ .The circle has the radius equal to $1$ and components parallel to $y-axis$ never exceeds the total length .

Therefore, the value of $\sin s$ is between $-1and1$ because the range of the unit circle is from $-1$ to $1$ .