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Chapter 7: Q. 98 (page 466)

f(x)=cotx

(a) Solve f(x)=-3.

(b) For what values of x is f(x)>-3 on the interval [0,蟺]?

Short Answer

Expert verified

(a) The solution is x|x=-蟺6+n蟺,nisaninteger.

(b) The solution set is -蟺6,2蟺3.

Step by step solution

01

Step 1. Given Information 

f(x)=cotx

(a) Solve f(x)=-3

(b) For what values of x is f(x)>-3on the interval [0,蟺]?

02

Part (a) Step 1. The given equation is f(x)=cotx

Putting f(x)=-3

-3=cotxcotx=-3

03

Part (a) Step 2. The solution for f(x)=-3.

胃=-蟺6

The solution is x|x=-蟺6+n蟺,nisaninteger.

04

Step (b) Part 1. The values of x is f(x)>-3 on the interval [0,π]

胃=-蟺6,2蟺3

The solution set is-蟺6,2蟺3.

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Most popular questions from this chapter

Establish each identity.

1-2cos2胃sin胃cos胃=tan胃-cot胃

Rewrite in terms of sine and cosine functions: cot(胃)sec(胃)

True or False:

tan2胃+tan2胃=tan4胃

Establish each identity.

sec2v-tan2v+tanvsecv=sinv+cosv

Establish each identity.

sin3胃+cos3胃1-2cos2胃=sec胃-sin胃tan胃-1
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