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Chapter 6: Q. 90 (page 381)

Iff(x)=cos胃=0.3,findrole="math" localid="1647539382705" f(胃+蟺)

Short Answer

Expert verified

The value off(胃+蟺)=-0.3

Step by step solution

01

Step 1. Given information

f(胃)=cos胃=0.3

02

Step 2. Finding the value of f(θ+π)

For an angle 胃is standard position,let P=(x,y)be the point on the terminal side of 胃that is also on the circle localid="1647539950698" x2+y2=r2.Then

localid="1647539956108" sin胃=yrcos胃=xrtan胃=yxcsc胃=rysec胃=rxcot胃=xy

Consider f(胃)==cos胃=0.3

That is cos胃=xr=0.3

sothat x is positive

therefore,胃is in 1st quadrants

Then 胃+蟺 is in the 2nd and 3rd quadrant so that xis negtive

Hence,

localid="1647539987909" f(胃+蟺)=-xr=-cos胃=-0.3

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Most popular questions from this chapter

In Example 6, we found that the distance between Albuquerque, New Mexico, and Glasgow, Montana, is approximately 903 miles. According to mapquest.com, the distance is approximately 1300 miles. What might account for the difference?

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