ketz
  • ketz
Can anybody explain tom me why when solving cos x >0.69? ...The answer is x<46.4 degrees?? why the inequality sign changes?
Mathematics
schrodinger
  • schrodinger
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kc_kennylau
  • kc_kennylau
Do you have the graph of cosine?
kc_kennylau
  • kc_kennylau
Actually, the value of cosine goes down when x goes up
ketz
  • ketz
So inequality signs are not only supposed to be flipped when divide by negative number or multiply by negative number??

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ketz
  • ketz
I thought it was only for the condition i stated above that inequality changes sign!!
kc_kennylau
  • kc_kennylau
Well, there are many conditions in which the inequality changes sign
kc_kennylau
  • kc_kennylau
You aren't multiplying something to the inequality here
ketz
  • ketz
Can you enumerate all of them please...
kc_kennylau
  • kc_kennylau
Well, in general, when you apply decreasing functions to both sides of an inequality, it changes signs.
kc_kennylau
  • kc_kennylau
Decreasing functions are those whose graphs go down.
kc_kennylau
  • kc_kennylau
|dw:1434221346342:dw|
kc_kennylau
  • kc_kennylau
This is a part of the cosine graph
kc_kennylau
  • kc_kennylau
You can see that if \(\cos x > 0.69\), \(x < \ \)something.
ketz
  • ketz
Thxs...Is there any other conditions to change the inequality sign? Can you provide a link...
kc_kennylau
  • kc_kennylau
Okay, those functions are called "decreasing functions". I'm searching for a list.
kc_kennylau
  • kc_kennylau
I can't really find a list available...
ketz
  • ketz
but how do you know all of them?
kc_kennylau
  • kc_kennylau
I can't know all of them, but in the case of cosine, I know the shape of the cosine graph.

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