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File: 62f2b3b7b7b09276a4ad01f2_Unit Circle Degrees.gif ( 58.82 KB , 1024x1024 , 1680066461904.gif )

Image
  No. 366
>>622 >>623 >>625 >>656
what's the most important trig concept you remember?
>>
  No. 367 >>624
I have a question on trigonometric hoping that is not OT: why in trig or, in general, in the module concept the number of cycles s is not considered?
for example: why 6 (mod 5) = 1 (mod 5) and is it not 11 (mod 5)?
>>
  No. 374 >>379
sinx=acsinx = \frac{a}{c}


cosx=bccosx = \frac{b}{c}


tgx=abtgx = \frac{a}{b}
(probabyl)

sin2x=1−cos2xsin^2x = 1 - cos^2x


tgx=sinxcosxtgx = \frac{sinx}{cosx}


That are the most important "axioms" for me though. They helped me to get equation for coordinates of a sphere cut.
>>
  No. 379 >>383

File: 590px-Spiral_of_Theodorus.svg.png ( 32.94 KB , 590x480 , 1680757562352.png )

Image
>>374

ever do anything with this?

https://en.wikipedia.org/wiki/Spiral_of_Theodorus
>>
  No. 383
>>379
No, it was to get spherical coords (I mean longitude and latitude) of some plane cutting this sphere.
It had parameters like:
-
11
- radius of shpere
-
λ0,ϕ0\lambda_0, \phi_0
- parameters of a point of a sphere which is intersection of a line perpendicular to the plane and sphere.
-
α\alpha
- where
cos(α)cos(\alpha)
is distance from plane to the center of the sphere

I don't remember it now, but I remember that distance
δ\delta
from
[0;0][0;0]
to
[ϕ;λ][\phi;\lambda]
was something like this:

cos(δ)=cos(λ)cos(ϕ)cos(\delta) = cos(\lambda)cos(\phi)


but I don't remember if it's really true even though it was a very nice and simple solution.
>>
  No. 622

File: 0e57cbec4c7a41c057547d562c66aa97.png ( 401.29 KB , 1202x1263 , 1705876095434.png )

Image
>>366
They're all equally important. You need to know all of it so you have the best chance at finding the best u and v in an integral question.
>>
  No. 623 >>624
>>366
That the squares of sine and cosine sum to 1. Or rather that R[sin,cos] is but R[x,y]/(1-x^2-y^2).
>>
  No. 624 >>654
>>623
True, because that equation creates the whole unit circle.

>>367
Moduloing by m partitions the number line into m partitions. 6, being 1m + 1, is equivalent to 11 because it's 2m + 1. Your number of cycles would be the multiplier of m.
>>
  No. 625

File: aed06f9a626ed4a0dfa92e186c44f458.png ( 1.58 MB , 868x1228 , 1705903015096.png )

Image
>>366
Writing sin and cos in terms of exponentials has served me quite well in complex analysis lol :)
>>
  No. 654
>>624
Well, but actually 11 is in base 5 and not in base 10 in fact you wrote 6 in base 10, being 1m+1 that have an extra turn that it is not counted, why?
>>
  No. 656
>>366
pythagoras

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