TheAspiringDoc's Math Thread

[ldunn]

To be clear, those sine arguments are in degrees, right? I make all of those expressions to be zero, which makes sense to me... not for the reasons mentioned earlier, though. It's just because of the symmetry involved. Each term has a corresponding term which is just the negative: sin(359) = -sin(1), sin(358) = -sin(2), etc.


^{Maybe I'm off my head, though}

[kinslayer]

To be clear, those sine arguments are in degrees, right? I make all of those expressions to be zero, which makes sense to me... not for the reasons mentioned earlier, though. It's just because of the symmetry involved. Each term has a corresponding term which is just the negative: sin(359) = -sin(1), sin(358) = -sin(2), etc.


^{Maybe I'm off my head, though}

Yep -- provided those are degrees, each expression is definitely equal to zero.

TheAspiringDoc, switch your calculator to degrees, or multiply the arguments by .

[TheAspiringDoc]

Yep -- provided those are degrees, each expression is definitely equal to zero.

TheAspiringDoc, switch your calculator to degrees, or multiply the arguments by .

I'd always been talking degrees?
And in that case they're all equal?

[kinslayer]

I'd always been talking degrees?
And in that case they're all equal?

Yes, they are equal to zero. This is because (in radians):



which is essentially what ldunn noted.

[TheAspiringDoc]

 Just wondering if someone could explain to me the applications of De Moivre's Formula?
Also, does Fermat's Last Theorem apply to complex numbers?
Thanks
P.S. Did you know the (5 or more)! always has a units digit of 0? This is beacause it contains 2 and 5, and when they are multiplied you get 10 and 10 times anything = 0 in the units column.

[TheAspiringDoc]

Express x in terms of a if ?

[cosine]

Express x in terms of a if

[TheAspiringDoc]

But my textbook says that's not the same is it?

[cosine]

But my textbook says that's not the same is it?

It's the same thing, but just different lay out to it

[keltingmeith]

It's the same thing, but just different lay out to it

Conjecture:



We evaluate:



And so, we see that they are only the same thing if a=0,2.

[cosine]

Conjecture:



We evaluate:



And so, we see that they are only the same thing if a=0,2.

Not really relevant to me, AspiringDoc asked why the book had a different lay out, I showed him why. I don't think he asked about what a can, and cannot equal?

[TheAspiringDoc]

Not really relevant to me, AspiringDoc asked why the book had a different lay out, I showed him why. I don't think he asked about what a can, and cannot equal?

Still, it's from an extension maths book so the more maths the better.

[keltingmeith]

Not really relevant to me, AspiringDoc asked why the book had a different lay out, I showed him why. I don't think he asked about what a can, and cannot equal?

No, you misunderstand. You said that:

=

But, I just showed that this is only true for a=0,2. However, it never said that a had to be restricted to those values, so what you've written is false.

[cosine]

No, you misunderstand. You said that:

But, I just showed that this is only true for a=0,2. However, it never said that a had to be restricted to those values, so what you've written is false.

What values are you referring to? I don't recall restricting anything to certain values, i left it as it was until you started to complicate things about the restrictions on a..

Besides it said express x in terms of a, hence no restrictions are involved as the only thing we are required to do is find an expression of x that is in expressed in a. When you write log(x) by itself, you don't usually write log(x), x cannot equal zero do you?

[keltingmeith]

What values are you referring to? I don't recall restricting anything to certain values, i left it as it was until you started to complicate things about the restrictions on a..

Besides it said express x in terms of a, hence no restrictions are involved as the only thing we are required to do is find an expression of x that is in expressed in a. When you write log(x) by itself, you don't usually write log(x), x cannot equal zero do you?

That's my point - what you've written is only true for a=0,2. For you to state that (which you did), then it HAS to be true for all a. It's not. What you've written is wrong.