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Chapter 7: Q. 13 (page 465)

In Problems 11鈥�34, solve each equation on the interval 0鈮�胃鈮�2蟺.

4cos2胃=1

Short Answer

Expert verified

The solution set is蟺3,2蟺34蟺3,5蟺3

Step by step solution

01

Step 1. Given Information

In the given problem we have to solve each equation on the interval0鈮�胃鈮�2蟺.

4cos2胃=1

02

Step 2. Firstly solving the equation4cos2θ=1

Divide by 4 on both side

44cos2胃=14cos2胃=14

Taking square root on both side

role="math" localid="1646566212432" cos胃=卤14cos胃=卤12

cos胃=12andcos胃=-12

03

Step 3. After solving the equationcosθ=12 and cosθ=-12

The period of the cosine function cos胃=12is 2蟺. In the interval [0,2蟺), there are two angles 胃for which

cos胃=12:胃=蟺3and胃=5蟺3

04

Step 4. The period of the cosine function cosθ=-12 is 2π.

In the interval [0,2蟺), there are two angles 胃for which cos胃=-12:胃=2蟺3and胃=4蟺3

So the solution set is蟺3,2蟺34蟺3,5蟺3

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Most popular questions from this chapter

Show that the difference quotient for f(x)=cosxis given by


role="math" localid="1646431168099" f(x+h)-f(x)h=cos(x+h)-cos(x)h=-sinx路sinhh-cosx路1-coshh

If z=tan伪2, show that localid="1646416257885" cos伪=1-z21+z2.

In Problems 9鈥�36, find the exact value of each expression.

cos-1sin5蟺4

if sin胃=45and 胃is in quadrant 2, thencos胃=______

Establish each identity.

1+sin胃1-sin胃=(sec胃+tan胃)2
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