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

1. kc_kennylau

Do you have the graph of cosine?

2. kc_kennylau

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

3. ketz

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

4. ketz

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

5. kc_kennylau

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

6. kc_kennylau

You aren't multiplying something to the inequality here

7. ketz

Can you enumerate all of them please...

8. kc_kennylau

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

9. kc_kennylau

Decreasing functions are those whose graphs go down.

10. kc_kennylau

|dw:1434221346342:dw|

11. kc_kennylau

This is a part of the cosine graph

12. kc_kennylau

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

13. ketz

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

14. kc_kennylau

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

15. kc_kennylau

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

16. ketz

but how do you know all of them?

17. kc_kennylau

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