Question

Use a graphing utility. Intervals are [0,2π) and we have to solve up to three decimal places?
To solve: 2 x cos x - 2 = 0. Can anyone please explain what will be the roots?

Answer 1

well it says *use a graphing utility* so just use a graphing calculator

Answer 2

\(\bf 2xcos(x)-2?\quad or\quad 2xcos(x-2)?\)

Answer 3

The first one, Jdoe.

Answer 4

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyeCpjb3MoeCktMiIsImNvbG9yIjoiI0RFMUIxQiJ9LHsidHlwZSI6MTAwMH1d <----

Answer 5

you can drag the graph with the mouse
and you can zoom in/out with the middle-button in the mouse

Answer 6

Solving for x, we will get three answers? Since the line is intercepting x-axis three times.

Answer 7

well, you can get an infinite amount of answers.... since usually the cosine function goes on both directions to infinity

but your constraints are \(\large [0, 2\pi)\)

Answer 8

Thank you for the help. Very kind of you!

Answer 9

Jde, can you point out what the answers will be? I need to match them. I'm certain I'm getting one of them wrong. Thanks!

Answer 10

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyeCpjb3MoeCktMiIsImNvbG9yIjoiI0RFMUIxQiJ9LHsidHlwZSI6MywiZXEiOltbIjYuMjgiLCIwIl1dLCJjb2xvciI6IiMyQzE0RTAifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyI0LjY2NTUyNTAzMjk2IiwiNi40MTAzNTU0OTY5NTk5OTkiLCItMC42ODU0NDUyODM4NDAwMDA0IiwiMC4zODgyOTY1NDAxNTk5OTk3NiJdfV0- <---- the blue dot, will be the 6.28, or \(\large 2\pi\) boundary

the graph doesn't touch the x-axis between 0 and farther to the right, up until 4.92 or so as you can see there

Answer 11

well.. you're supposed to solve up to 3 decimals places... well.. you can just zoom in further I guess -> http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyeCpjb3MoeCktMiIsImNvbG9yIjoiI0RFMUIxQiJ9LHsidHlwZSI6MywiZXEiOltbIjYuMjgiLCIwIl1dLCJjb2xvciI6IiMyQzE0RTAifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyI0LjY2NTUyNTAzMjk2IiwiNi40MTAzNTU0OTY5NTk5OTkiLCItMC42ODU0NDUyODM4NDAwMDA0IiwiMC4zODgyOTY1NDAxNTk5OTk3NiJdfV0-

Answer 12

Understood. Thank you very much, sir.

Answer 13

yw