cosx=10/x

[quader]

Draw a sketch of

Determine the number of roots of the equation which lie in the interval -180<x<180.



I have no clue how to sketch this one, but it says the answer is 3.

 

[HallsofIvy]

Do you know what the graph of y= cos(x) looks like? y= 10/x is a hyperbola. Graph those two functions on the same axes and see where they cross. With so much graphing technology available, it seems strange that you cannot graph them. A basic but nice graphing program can be downloaded for free at http://www.padowan.dk/

 

[quader]

Okay, thank you. I did graph them, but this is what I get:



It doesn't cross 3 times between the points...

 

[Ishuda]

Convert the \(\displaystyle x^\circ\) (x in degrees) to radians, i.e.
cos(\(\displaystyle \frac{\pi}{180} x\)) = 10/x
and be careful of the possible false crossing near zero depending on graph software.

 

[HallsofIvy]

In addition to converting from degrees to radians, since your graphing program is assuming the angles are in radians, you should understand that cos(x) will never be larger than 1 so you cannot expect to see 10/x crossing it until x is larger than 10. Change the scale or the beginning x values for your graph.