Question

CRITICAL THINKING

A function is called even if the graphs of $y=f\left(x\right)$and

$y=f(-x)$ are exactly the same. Which of the six trigonometric functions are

even? Justify your answer with a graph of each function.

Short answer

Only cosine and sec functions are even

Step-by-step solution

Step 1. Given information

Even function definition is given.

Step 2. Concept used

Draw the graph of each function and check the answer.

Step 3. Calculation

The graph of cosine and negative of cosine function as-

The graph of sec and negative of sec function as-

the graph of sine function-

The graph of tangent function-

The graph of cosec function-

The graph of cot function-

From the above graphs we conclude that only cosine and sec functions are even.