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Chapter 7: Q. 119 (page 468)

Explain in your own words how you would use your calculator to solve the equation cosx=-0.6,0鈮�x鈮�2蟺. How would you modify your approach to solve the equation cotx=-0.6,0鈮�x鈮�2蟺?

Short Answer

Expert verified

The solution set ofcosx=-0.6is2.21,4.07 andcotx=-0.6is0.197,3.337.

Step by step solution

01

Step 1. Given Information 

Explain in your own words how you would use your calculator to solve the equation cosx=-0.6,0鈮�x鈮�2蟺. How would you modify your approach to solve the equation cotx=-0.6,0鈮�x鈮�2蟺?

02

Step 2. To solve cos x=-0.6, 0≤x≤2πon a calculator,

First set the mode to radians. Then use the cos-1key to obtain

x=cos-1-0.6

x鈮�2.214

Rounded to two decimal places, 2.21radian.

03

Step 3. Since cosine function is positive in fourth quadrant so we can use the identify cos2π-θ=cosθ

To find the second solution within [0,2蟺]

x=2蟺-2.21x=4.07

Then the solution set isrole="math" localid="1647109842173" 2.21,4.07.

04

Step 4. To solve cotx=-0.6 on calsulator.

We firstly write cotx=1tanx

Then the equation is

1tanx=51tanx路tanx=5路tanx1=5路tanx15=55路tanxtanx=0.2

use the cot-1key to obtain.

05

Step 5. Now First set the mode to radians. Then use the tan-1 key to obtain.

x=tan-10.2x鈮�0.197

Rounded to two decimal places, 0.19radian.

06

Step 6. Since tangent function is positive in third quadrant so we can use the identify tanπ+θ=tanθ

To find the second solution within[0,2蟺]

x=蟺+0.197x=3.337

Then the solution set is0.197,3.337

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