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Chapter 6: Q 125 (page 397)

Show that the period off(胃)=sec胃is2蟺.

Short Answer

Expert verified

From the following graph of secant function f(胃)=sec胃it is clear that the period of secant function is 2蟺.

Step by step solution

01

Step 1. Given Information

We have to prove that the period of secant function is 2蟺.

We will draw the graph of this function. After that from the graph we will examine the period of the function.

02

Step 2. To find period of secant function  

The given function is :-

f(胃)=sec胃.

By using graphing utilities, we have the following graph of this function :-

We can see that curve of the graph repeated itself.

We know that the period of a function is where from the graph of function repeated itself.

We can see that the graph from 0to 2蟺is same as 2蟺to 4蟺and -2蟺to 0.

So we can conclude that the period of the given function is 2蟺.

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Most popular questions from this chapter

Difference in Time of Sunrise Naples, Florida, is approximately 90 miles due west of Ft. Lauderdale. How much sooner would a person in Ft. Lauderdale first see the rising Sun than a person in Naples? See the hint. [Hint: Consult the figure. When a person at Q sees the first rays of the Sun, a person at P is still in the dark. The person at P sees the first rays after Earth has rotated so that P is at the location Q. Now use the fact that at the latitude of Ft. Lauderdale in 24 hours an arc of length 2蟺3559miles is subtended.]

Find the exact value of each expression. Do not use a calculator.

2sec蟺4+4cot蟺3

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Write the equation of a sine function that has the given characteristics.

Amplitude: 4

Period:1
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