Chapter 14.1, Problem 36PPS

a.

To determine

To complete the given table.

Explanation of Solution

Given:

The given table is-

  

Calculation:

The following is the completed table-

  

b.

To determine

To use a graphing calculator to graph ${\tan }^2\theta -{\sin }^2\theta ={\tan }^2\theta {\sin }^2\theta$ as two separate functions. Sketch the graph.

Explanation of Solution

The following are the two separate graphs-

  

  

c.

To determine

To find whether the graphs coincide.

Explanation of Solution

From the above graph, it can be seen that the both graphs coincide for the same domain and range.

d.

To determine

To find whether the equation ${\sec }^{2}x-1={\sin }^{2}x{\sec }^{2}x$ is an identity using graphing calculator.

Explanation of Solution

Let us draw the graph of ${\sec }^{2}x-1$

  

Now let us draw the graph of ${\sin }^{2}x{\sec }^{2}x$

  

It can be seen that both the graphs coincide for the same domain and range.

Hence, the equation ${\sec }^{2}x-1={\sin }^{2}x{\sec }^{2}x$ is and identity.