Can anybody explain tom me why when solving cos x 0.69? ...The answer is x

Question

Can anybody explain tom me why when solving cos x >0.69? ...The answer is x<46.4 degrees?? why the inequality sign changes?

kc_kennylau · Answer

Do you have the graph of cosine?

kc_kennylau · Answer

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

ketz · Answer

So inequality signs are not only supposed to be flipped when divide by negative number or multiply by negative number??

ketz · Answer

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

kc_kennylau · Answer

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

kc_kennylau · Answer

You aren't multiplying something to the inequality here

ketz · Answer

Can you enumerate all of them please...

kc_kennylau · Answer

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

kc_kennylau · Answer

Decreasing functions are those whose graphs go down.

kc_kennylau · Answer

|dw:1434221346342:dw|

kc_kennylau · Answer

This is a part of the cosine graph

kc_kennylau · Answer

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

ketz · Answer

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

kc_kennylau · Answer

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

kc_kennylau · Answer

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

ketz · Answer

but how do you know all of them?

kc_kennylau · Answer

I can't know all of them, but in the case of cosine, I know the shape of the cosine graph.