@AbhasKumarSinha I think you are confused. The sine and cosine have nothing to do with degrees. Degrees is a unit. It's the same as if you say the parabola has to do with meters...
It's weird that i have not defined the tangent function yet.
how do i prove that $\sin(\pi/4)=\cos(\pi/4)$?
I have prove that $\tan:(-\pi/2,\pi/2)\rightarrow\mathbb{R}$ is a strictly increasing continuous bijection. (Not yet proved that it's a homeomorphism; i think i can show that arctan is co...
So you've asked for example why $\pi = 180$. This is of course not true, as $\pi = 3,14159265... \neq 180$. What we say is that $\pi$ radians $= 180$ degrees.
"Determine the coefficients $a_n$ such that the function $$u(r,\theta) = \sum_{-\infty}^{\infty} a_n r^{|n|} e^{i n \theta}, \: 0 \leq r \leq 1, \: 0 \leq \theta 2 \pi$$ satisfies $u(1,\theta) = \delta(\theta - \theta_0)$
So if you take 45 pieces of the sector that is used to define degrees, you get 45 degrees. But you need much less pieces of the sector that is used to define radians in order to construct a sector of the same area, because the sector corresponding to 1 radian is bigger than that of 1 degrees
For example in a equation (as an example) - $\sin x = \sin (90 - x)$, I can cancel sin both sides? or not? But. why I can't do cancellation here $\sin \frac{\pi}{4} radians = \45 deg$ here I can't cancel sin from both sides. Why?
But for something to be cancellation, it has to always work, regardless of what value of $x$ is. This is clearly not true in the above case, hence it is not a cancellation
yes, sin is basically a machine that spits out a ratio when given a number, thus it is not a number as the outcome will change depending on what you feed into it
@Secret okay, that's not cancellation, its something inside the input of functions to be performed before the calculation of values of function to get the value ? @Secret
@abenthy I think this should be true... checking the injectivity of the map $G(\mathbb{Q}) \rightarrow G(\mathbb{R})$ amounts to checking that if you have maps $f,g: A \rightarrow \mathbb{Q}$ inducing the same map after composing the map $\mathbb{Q} \hookrightarrow \mathbb{R}$ (where $A$ is any $\mathbb{Q}$-algebra), then $f=g$, but I think this is just set theory..
@AbhasKumarSinha we can approximate trig functions as polynomial functions. Calculators can then use these to very very efficiently calculate trig functions to many decimal places
There are also some methods that allow you to calculate certain values of trig functions using different identities
As I understand it... ahem... the (cosine, sine) vector was calculated for (30 degrees, PI/6), (45 degrees, PI/4) and (60 degrees, PI/3) angles etcetera, however, I would like know the original geometrical process for calculating the magnitudes for each vector in the trigonometric lookup table.
...
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.
The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory.
In formulas, a limit is usually written as
lim
n
→
c
f
...
Just with those operations, no. It turns out that sine is what's called a "transcendental function", and one of the consequences of being a transcendental function is that it can't be written as a finite combination of non-transcendental things
(such as plus, minus, times, division, exponentiation, and roots)