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Chapter 6: Q 111 (page 396)

Is the secant function even, odd, or neither? Is its graph symmetric? With respect to what?

Short Answer

Expert verified

The secant function is an evenfunction.

It is symmetrical about y-axis.

Step by step solution

01

Step 1. Given Information

We have to check that the secant function is an even function, odd function or neither.

Also we have to check that it is symmetric or not.

If yes, then we also to find that it is symmetric about what.

02

Step 2. To check that Secant function is even, odd or neither.

We know that a function is even if f(-x)=f(x)and is odd if f(-x)=-f(x).

We also know that :-

sec-胃=sec胃.

So we can conclude that Secant function is an even function.

03

Step 3. To check about symmetric

To check the symmetry of the secant function we will use graphing utility.

By using graphing utility, we can graph the secant function as following :-

From the graph we can see that the graph is neither symmetric about x-axis nor origin, but it is symmetric about y-axis.

So we can conclude that secant function is symmetric about y-axis.

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Most popular questions from this chapter

An angle 胃is in ________ _________ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.

Is the tangent function even, odd, or neither? Is its graph symmetric? With respect to what?

What is the range of the tangent function?

Use a calculator to find the approximate value of each expression rounded to two decimal places:csc5蟺13

Two hallways, one of width 3feet, the other of width 4 feet, meet at a right angle.

See the illustration.

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role="math" localid="1646353783956" L(胃)=3sec胃+4csc胃

(b) Graph L=L(胃),0<胃<蟺2

(c) For what value of 胃is L the least?

(d) What is the length of the longest ladder that can be carried

around the corner? Why is this also the least value of L?
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