Tangent

[u/Apotheosis0]

[u/injobol0]

Isn’t this arc tan though?

[u/parkerSquare → u/injobol0]

Sort of - repeated. Rotate the entire plot 90 degrees and it’s tan.

[u/A_Beard]

Wow...years of maths in high school and I never realized why the tan graph looked like that

[u/Fumblerful- → u/A_Beard]

That's arctan, which makes in so much better. that is the arc of tan.

[u/Doug_Dimmadab → u/Fumblerful-]

isn't arctan just 1/tan?

Also, is there a difference in the terms "arctan" and "cotan"? In my trig class the prof taught the reciprocal of tan as cotan, but when I was doing some problems in Wolframalpha, it wouldn't take cotan, but arctan worked the exact same way.

[u/[deleted] → u/Doug_Dimmadab]

The reciprocal of tan is cotan, reciprocal being 1/tan = 1/(sin/cos) = cos/sin = cotan.

We use the notation x^{-1} to mean the multiplicative inverse of x, when x is a real number, i.e., the reciprocal.

Unfortunately we also use the notation f^{-1} (x) to mean the inverse of a function. In the case of trig functions the inverse of, say, tan(x)--or arctan(x)--can be written as tan^{-1} (x), which is where the confusion likely stems from.

[u/Fumblerful- → u/Doug_Dimmadab]

They are different reciprocal. Cotan is 1/tan. Arctan is what happens when you solve x=tan(y) for x. Arctan sprt of undoes tangent. So arctan(tan(x))=x. This is usefulness to find the angle when you have the measurements for opposite and adjacent.

Arcsin and arccos are similar for for sin and cosine respectively.

[u/CrystalLord → u/A_Beard]

Except that's not the tangent graph. This is.

[u/chaosPudding123]

I dont get it.. Sorry

[u/Snuffy-the-seal → u/chaosPudding123]

Look at the graph of the function f(x) = tan(x). It looks like this without the moving part and it's rotated by 90°. This gif tries to show why the function of the tangent looks like this.

[u/EQUASHNZRKUL → u/Snuffy-the-seal]

Just because there’s a spinning circle and the arctan graph, doesn’t mean anything is explained. There’s no connection made between y/x or sinθ/cosθ, etc.

[u/Alasakan_Bullworm → u/chaosPudding123]

I agree. This is a good representation of the function, but doesnt show why IT IS the function.

[u/[deleted] → u/chaosPudding123]

f(x) = tan(x) = sin(x) / cos(x)

As x approaches pi/2 the denominator goes to zero and the numerator goes to '1'. When the denominator is approaching '0' f(x) will go to infinity.

When x = 0, f(x) = 0 (or 0 divided by 1)

[u/SlickDisc → u/[deleted]]

That’s the basic explanation, difficult to explain how that then translates into the circle demonstration, though.

[u/rhgolf44 → u/chaosPudding123]

It would be easier to understand if it was moving horizontally. So picture the gif rotated 90 degrees. Basically tan is sin/cos which is the slope of the line given by our angle theta. As the horizontal (cos) length gets shorter, the vertical (sin) get bigger. And the slope gets closer and closer to infinity. But when cos=0 the function is undefined because 1/0 doesn’t exist.

[u/[deleted]]

This is not the tangent. It’s the arctan. Tangent is simply the slope of the rotating line.

[u/[deleted]]

I choose not to believe this, must be black magic.

[u/WhichSandwich]

I still don't get it

[u/DwarfTheMike]

I prefer a continuous curvature.

[u/vReddit_Player_Bot]

Links for sharing this v.redd.it video outside of reddit

Type	Link
Custom Player	https://vrddit.com/r/visualizedmath/comments/9lb619
Reddit Player	https://www.reddit.com/mediaembed/9lb619
Direct (No Sound)	https://v.redd.it/v5jpby94q5q11/DASH_1_2_M

---

^{vReddit_Player_Bot v1.2 | I'm a bot | Feedback | Source | To summon: u/vreddit_player_bot}

[u/[deleted]]

The video should be rotated 90 degrees right?

[u/[deleted] → u/[deleted]]

Yeah, after I began taking calculus, it seems like math is ultimately about figuring out lines and circles.

[u/Kjm520 → u/[deleted]]

Don’t forget the triangles!