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Chapter 7: Q. 28 (page 465)

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

5csc胃-3=2

Short Answer

Expert verified

The solution set is蟺2.

Step by step solution

01

Step 1. Given Information 

In the given problem we have to solve each equation on the interval 0鈮�胃鈮�2蟺

5csc胃-3=2

02

Step 2. Firstly solving the equation 

Add 3 on both side

5csc胃-3+3=2+35csc胃=5

Divide by 5 on both side

55csc胃=55csc胃=1

03

Step 3. After solving the equation cscθ=1

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

csc胃=1:胃=蟺2

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Most popular questions from this chapter

tan2胃-sec2胃

True or False. sin2胃has two equivalent forms:

2sinucosuand sin2胃-cos2胃

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.

Sawtooth Curve An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes. A first approximation to the sawtooth curve is given by

y=12sin(2蟺x)+14sin(4蟺x)

Show thaty=sin(2蟺x)cos2(蟺x)

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

seccos-112
See all solutions

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