#### MethMath11

##### Junior Member
What's the meaning of let.... I really don't know what it means (my vocab are limited)
Can anyone explain it to me?

#### Harry_the_cat

##### Senior Member
$$\displaystyle x\in[a, b]$$ means the same as $$\displaystyle a\leq{x}\leq{b}$$.

$$\displaystyle x\in(a, b)$$ means the same as $$\displaystyle a<x<b$$.

Note one has square brackets and the other has round brackets to either include or exclude a and b.

It is used here as a way of stating the domain.

#### MethMath11

##### Junior Member
$$\displaystyle x\in[a, b]$$ means the same as $$\displaystyle a\leqx\leqb$$.

$$\displaystyle x\in(a, b)$$ means the same as $$\displaystyle a<x<b$$.

Note one has square brackets and the other has round brackets to either include or exclude a and b.
Now that I know what it means. Sorry to bother you, is there any need for me to turn f(x) into an f'(x) in this question?

#### Dr.Peterson

##### Elite Member
When in math we say "Let x = 4", or something like that, it means "Suppose that x = 4". Literally, it can be thought of as "Make x be 4", that is, a definition of the variable. That's the closest to this usage I find in a dictionary, apart from this one that explicitly states the mathematical usage:

5 [transitive] [usually in imperative] maths used in mathematics for saying that you are imagining that something is true, usually in order to prove a principle of mathematics​
Let x = 5.​
Let ABC be a triangle.​

Here, it's the same idea, though not quite a definition: "Suppose that x is in the interval ...".

#### MethMath11

##### Junior Member
I only know
$$\displaystyle x\in[a, b]$$ means the same as $$\displaystyle a\leq{x}\leq{b}$$.

$$\displaystyle x\in(a, b)$$ means the same as $$\displaystyle a<x<b$$.

Note one has square brackets and the other has round brackets to either include or exclude a and b.

It is used here as a way of stating the domain.
I only know how to get the maximum number from a 1 trig, ex f(x) = cos2x or something like that, is there any link for me to study this equation?

#### Harry_the_cat

##### Senior Member
You can find the max using calculus (ie finding f'(x)) OR by considering what the graph looks like.

#### Harry_the_cat

##### Senior Member
When in math we say "Let x = 4", or something like that, it means "Suppose that x = 4". Literally, it can be thought of as "Make x be 4", that is, a definition of the variable. That's the closest to this usage I find in a dictionary, apart from this one that explicitly states the mathematical usage:

5 [transitive] [usually in imperative] maths used in mathematics for saying that you are imagining that something is true, usually in order to prove a principle of mathematics​
Let x = 5.​
Let ABC be a triangle.​

Here, it's the same idea, though not quite a definition: "Suppose that x is in the interval ...".
I took it that MethMath11 was asking what was meant by the symbolism after the "let".

#### Dr.Peterson

##### Elite Member
Since the question mentioned vocabulary, my first impression was that the question was about the word (or the entire phrase); after seeing your response, I thought it would be still good to deal with the word too. But apparently you're right.

#### MethMath11

##### Junior Member
Can anyone help me with the formula, I forgot what sub-chapter the formula is,, but it's something like if it's cos, then the max is either at 90° or 270°, and then the formula is 90 = k.360 + x u think, can't remember it, can anyone help me?

#### MethMath11

##### Junior Member
You can find the max using calculus (ie finding f'(x)) OR by considering what the graph looks like.
I really have no idea what to do with the sec except turning it into a 1 + tan

#### Dr.Peterson

##### Elite Member
Can anyone help me with the formula, I forgot what sub-chapter the formula is,, but it's something like if it's cos, then the max is either at 90° or 270°, and then the formula is 90 = k.360 + x I think, can't remember it, can anyone help me?
What formula are you asking about? If you're trying to list all points where cosine has its maximum, that's not going to help here, at least not yet. But since the problem is written in radians, you shouldn't be using degrees anyway.

I really have no idea what to do with the sec except turning it into a 1 + tan
What sec?? And I hope you aren't saying that sec x = 1 + tan x.

As for solving the problem, one trick I see is to substitute x + pi/6 = u. That will at least make it a lot easier to work with the derivatives.

Please show what you've tried with the derivative (or any other method), so we can see what help you need.

On the other hand, are you allowed to use any tools such as a graphing calculator? Having checked the graph, I see that would save you a lot of work.

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#### MethMath11

##### Junior Member
I
What formula are you asking about? If you're trying to list all points where cosine has its maximum, that's not going to help here, at least not yet. But since the problem is written in radians, you shouldn't be using degrees anyway.

What sec?? And I hope you aren't saying that sec x = 1 + tan x.

As for solving the problem, one trick I see is to substitute x + pi/6 = u. That will at least make it a lot easier to work with the derivatives.

Please show what you've tried with the derivative (or any other method), so we can see what help you need.
It's sec^2 = 1+tan^2 x

#### MethMath11

##### Junior Member
What formula are you asking about? If you're trying to list all points where cosine has its maximum, that's not going to help here, at least not yet. But since the problem is written in radians, you shouldn't be using degrees anyway.

What sec?? And I hope you aren't saying that sec x = 1 + tan x.

As for solving the problem, one trick I see is to substitute x + pi/6 = u. That will at least make it a lot easier to work with the derivatives.

Please show what you've tried with the derivative (or any other method), so we can see what help you need.
Y' = sec^2 (x + 2π/3) - sec^2 ( x + π/6) - sin ( x + π/6

#### Dr.Peterson

##### Elite Member
Try my substitution. I don't see that that makes it easy, but it does make it easier. (This is why I asked about using technology.)

#### MethMath11

##### Junior Member
Try my substitution. I don't see that that makes it easy, but it does make it easier. (This is why I asked about using technology.)
There's a problem with converting x + π/6 = u, how about the X +2π/3 ?