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Chapter 7: Q. 34 (page 465)

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

role="math" localid="1646669697147" cos胃3-蟺4=12

Short Answer

Expert verified

The solution set is7蟺4.

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cos胃3-蟺4=12

02

Step 2. In the interval [0,2π), the cosine function 12 equals at  π3

So, we know that 胃3-蟺4must equal 蟺3.

To find these solutions, write the general formula that gives all the solutions.

胃3-蟺4=蟺3+2蟺苍

Add 蟺4on both side

胃3-蟺4+蟺4=蟺3+2蟺苍+蟺4胃3=蟺3路44+2蟺苍路1212+蟺4路33胃3=4蟺12+12蟺苍12+3蟺12胃3=4蟺+12蟺苍+3蟺12胃3=7蟺+12蟺苍12

Multiply with 3 on both side

胃3脳3=7蟺+12蟺苍12脳3胃=7蟺+12蟺苍4

03

Step 3. The general formula is θ=7π+12πn4

So the value of given function in interval [0,2蟺)is

胃=7蟺+12蟺脳04胃=7蟺4

So the solution set is7蟺4.

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