5
votes
2answers
92 views

Hyberbolic and Circular (Trig) Functions: Why no parabolic? [duplicate]

There are circular (trig) functions which determine all the points on a unit circle: and which relate to the area swept out by an angle subtended on the circle. -- These functions can of course be ...
1
vote
6answers
85 views

What is one way to prove that there exists no ellipse that matches the exact curvature of the sin wave?

Preferably by not graphing both and showing they don't match visually. By the sin wave, I mean just plain old y=sinx.
0
votes
0answers
125 views

Find points of intersection with cone on a plane at a given angles

The provided variables are the cone angle(cA) of a cone that starts at the origin along the Z axis, the vertical angle (vA) of the direction the cone is facing, and a horizontal angle (hA) along with ...
0
votes
0answers
29 views

How are the sine functions along with the hyperbolic functions visualized with imaginary rotations?

Since we know that: cos(t)=cosh(it) and isin(t)=sinh(it) I've been thinking about this, and obviously this is referring to how if you move at a right angle from a circle on a conic section, you end ...
2
votes
2answers
314 views

How to interpret angle of Ellipse in drawing guide?

Im a designer who, in my work, often uses drawing guides for drawing ellipses. A few nights ago I attempted to design some guides of my own but I was baffled as a I could not understand how to define ...
5
votes
1answer
594 views

Geometric construction of hyperbolic trigonometric functions

If we have a circle we can geometrically construct the trigonometric functions as shown. The functions all derive from sin and cos. If we say that the circle is a conic section and imagine it on the ...
1
vote
1answer
236 views

Find next point in ellipse given the chord length

I would like to draw a cloud programmatically. For this reason I need to know where to draw the next circle around the ellipse. Given the chord (circle radius), how can I calculate the next point in ...
1
vote
1answer
63 views

Find the equation of the hyperbola given foci and the minor axis

first time posting and using the site. I have a quick problem that I need some help with. I need to find the equation of a hyperbola given the foci and the length of the minor axis. The foci ...
3
votes
2answers
13k views

Ellipse in polar coordinates

I think Wikipedia's polar coordinate elliptical equation isn't correct. Here is my explanation: Imagine constants $a$ and $b$ in this format - Where $2a$ is the total height of the ellipse and $2b$ ...
4
votes
4answers
554 views

Getting the equation of an ellipse using the constant and the foci

Find the equation of the ellipse with the foci at (0,3) and (0, -3) for which the constant referred to in the definition is $6\sqrt{3}$ So I'm quite confused with this one, I know the answer is ...
4
votes
0answers
369 views

Calculating equidistant points around an ellipse arc

As an extension to this question on equiangular fisheye distortion, how can I calculate equidistant points around an ellipse (or 1/4 segment of) given it's aspect ratio? When it's circular, I can use ...
0
votes
1answer
1k views

Eccentricity of an ellipse

How is $\frac{PF}{PD} = e = \frac{C}{A}$ ? where e is eccentricity. What is the answer NOT using analytic geometry? (Using trigonometry) P stands for any point on the ellipse. $F$ stands for one of ...
35
votes
3answers
2k views

Do “Parabolic Trigonometric Functions” exist?

The parametric equation $$\begin{align*} x(t) &= \cos t\\ y(t) &= \sin t \end{align*}$$ traces the unit circle centered at the origin ($x^2+y^2=1$). Similarly, $$\begin{align*} x(t) ...
4
votes
3answers
2k views

Calculate intersection of two ellipses

I used the equations found here to calculate the intersection points of two circles: (P3 is what I'm trying to get) Except, now I want to do the same with two ellipses. Calculating ...
3
votes
3answers
1k views

Canonical to Parametric, Ellipse Equation

I've done some algebra tricks in this derivation and I'm not sure if it's okay to do those things. $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = \cos^2\theta + ...
14
votes
4answers
3k views

Aunt and Uncle's fuel oil tank dip stick problem

This problem first came to me in high school, and a couple times since, and I even assigned it for extra credit in one of my calculus classes after I became a teacher. So I know the solution. What I ...