/sci/ - Science & Math

[Anonymous No.6803429]

>mfw I realised that cosine is actually sine with 90 degrees phase shift

[Anonymous No.6803442]

Is that really your face? You don't look like a human at all.

[Anonymous No.6803480]

>>6803429
>not seeing that sin and cos are obviously just taken from another angle (90° apart)
also sin(x+π)=-sin(x)
and cos(x+π)=-cos(x) obviously

[Anonymous No.6803486]

>>6803442
le sinus faec

[Anonymous No.6804286]

The cofunction identities tell you this explicitly.

[Anonymous No.6804309]

Tfw the slope of the line on a sine graph can be expressed by the value of the cosine so long that the inside function is theta alone

[Anonymous No.6804318]

have you never heard of a unit circle?

[Anonymous No.6804333]

>>6803486
This is more perfect than the person writing it could have hoped for. One of the biggest problems the Mississippi faces is from a distinct lack of twists and turns.

[Anonymous No.6804684]

>tfw you realize <span class="math">\frac{1}{x^{2}+1}[/spoiler] is just a single, streched out period of <span class="math">cos^{2}\!(x)[/spoiler]
>tfw an infinite flood of trigonometric identities become obvious and apparent to you
>tfw you dream of being a triangle

[Anonymous No.6804719]

>>6803480
This image a shit.

[Anonymous No.6804749]

>tfw euler's formula

[Anonymous No.6804760]

>>6804684
So cos^2(x/a) converges to 1/(x^2+1) when a approaches infinity?

Is the proof trivial?

[Anonymous No.6804806]

>>6804760
cos^2(x/a) converges to 1 as a approaches infinity
1/(x^2+1) converges to 0 at infinite and negative infinity
the tangent function has vertical asymptotes at the ends of its period, so it shrinks 1/(x^2+1) down to its period, making pi/2 and -pi/2 0. this ends up being cos^2(x). it's relatively easy to prove too. just thought it was a neat relation and it helped me make the connection between tan^-1(x) and 1/(x^2+1), and other various identities.
i'll get some pics in a minute