Book about irrational inequalities and other....

[jedimath]

Good evening, I have consulted several precalculus books, intermediate algebra but none of these lists irrational inequalities, trigonometric inequalities and more. In which book I can find them? Thank you :)

 

[fresh_42]

What are irrational inequalities and which kind of book are you looking for? I haven't heard of trigonometric inequalities, except the triangle inequality and of course occasionally some in specific situations. You can find a lot of general inequalities on Wikipedia, but I still don't know what you mean.

 

[jim mcnamara]

Possibly identities - like trig identities?

 

[jedimath]

Hi, here an example:

$$\sqrt{x+1} + \sqrt{x + 6} > \sqrt{7x + 4}$$

and

$$\frac{4 senx^2 - 1}{2 cosx} >= 0$$

and so on. Yet...inequalites with absolute value.

Thanks.

 

[member 587159]

Hi, here an example:

$$\sqrt{x+1} + \sqrt{x + 6} > \sqrt{7x + 4}$$

and

$$\frac{4 senx^2 - 1}{2 cosx} >= 0$$

and so on. Yet...inequalites with absolute value.

Thanks.

I think these inequalities all follow from elementary calculus. Many problems in calculus books are devoted to proving such inequalities. E.g. Spivak' calculus contains much problems like these.

 

[Mark44]

Hi, here an example:

$$\sqrt{x+1} + \sqrt{x + 6} > \sqrt{7x + 4}$$

and

$$\frac{4 senx^2 - 1}{2 cosx} >= 0$$

and so on. Yet...inequalites with absolute value.

Thanks.

Many or most precalculus textbooks have problems similar to these, although they would probably be dealing with equations rather than inequalities. The main difference between equations and inequalities is that with inequalities, if you multiply both sides by an expression, the direction of the inequality changes if the expression you're multiplying by is negative.

I don't believe that there would be a textbook that deals solely with the inequalities you're asking about.