Concept explainers
To graph: The given trigonometric expression and determine which trigonometric function is equal to the expression. Then verify the resulting identity algebraically.

Explanation of Solution
Given information:
The following trigonometric expression:
Graph:
Sketch the graph using graphing utility.
Step 1: Press WINDOW button to access the Window editor.
Step 2: Press
Step 3: Enter the expression
Step 4: Press GRAPH button to graph the function.
The graph is obtained as:
Interpretation:
According to the above graph, it can be observed that the given expression has the same graph as obtained forsecant function. Hence,
Formula used:
The following identities:
The Pythagorean identity:
The Quotient identity:
The Reciprocal identities:
Proof:
The given trigonometric expression can be simplified as follows:
Therefore,
The simplified expression is same as the expression obtained from the graph. Hence, verified.
Chapter 5 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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