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Chapter 7: Q. 12 (page 465)

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

1-cos胃=12

Short Answer

Expert verified

The solution set is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.

1-cos胃=12

02

Step 2. Firstly solving the equation 1-cosθ=12

Subtract 1 on both side

1-cos胃-1=12-1-cos胃=12-1路22-cos胃=12-22-cos胃=1-22-cos胃=-12

Multiply with -1on both side

role="math" localid="1646565140078" -cos胃脳(-1)=-12脳(-1)cos胃=12

03

Step 3. After solving the equation cosθ=12

The period of the cosine function is 2蟺. In the interval [0,2蟺), there are two angles 胃for whichlocalid="1646566828893" cos胃=12:胃=蟺3and胃=5蟺3

So the solutions set is蟺3,5蟺3

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Most popular questions from this chapter

Multiply and simplify:(1+tan(胃))(1+tan(胃))-sec(胃)tan(胃)

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

cos2胃=cos2胃- = -1=1- .

A rectangle is inscribed in a semicircle of radius 1. See the illustration.

Part (a): Express the area A of the rectangle as a function of the angle 胃shown in the illustration.

Part (b): Show that A胃=sin2胃.

Part (c): Find the angle 胃 that results in the largest area A.

Part (d): Find the dimensions of this largest rectangle.

Show thatsin-1v+cos-1(v)=蟺2
See all solutions

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