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- 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?

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- ketz

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- kc_kennylau

Do you have the graph of cosine?

- kc_kennylau

Actually, the value of cosine goes down when x goes up

- 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

I thought it was only for the condition i stated above that inequality changes sign!!

- kc_kennylau

Well, there are many conditions in which the inequality changes sign

- kc_kennylau

You aren't multiplying something to the inequality here

- ketz

Can you enumerate all of them please...

- kc_kennylau

Well, in general, when you apply decreasing functions to both sides of an inequality, it changes signs.

- kc_kennylau

Decreasing functions are those whose graphs go down.

- kc_kennylau

|dw:1434221346342:dw|

- kc_kennylau

This is a part of the cosine graph

- kc_kennylau

You can see that if \(\cos x > 0.69\), \(x < \ \)something.

- ketz

Thxs...Is there any other conditions to change the inequality sign? Can you provide a link...

- kc_kennylau

Okay, those functions are called "decreasing functions". I'm searching for a list.

- kc_kennylau

I can't really find a list available...

- ketz

but how do you know all of them?

- 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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