# Tagged Questions

0answers
77 views

### What is this expression called?

Could anyone please tell me if they recognize this equation? What it does is calculate the angle between two lines, but I need it's name. Any help is greatly appreciated! \sin \theta = A_{1} \cdot ...
1answer
128 views

### How is the formula for the focal point of a ball lens derived?

In Optical Design Fundamentals for Infrared Systems 2nd ed., Mr. Riedl writes: A sphere or ball performs surprisingly well as a lens. At closer scrutiny, one fmds that such an element can be ...
1answer
62 views

### Restriction Of Parametric Functions Domain

The problem I am working on is, "Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the ...
1answer
34 views

### How to figure out x and y components of a vector

Given a vector $\vec{v}$ and an angle $\alpha$ between the vector and $Oy$ or $Ox$ what is the quickest way to figure out the projections, or the $x$ and $y$ components?
2answers
262 views

### Finding point coordinates of a perpendicular

Given that I know the point coordinates of point $A$ and point $B$ on segment $AB$ and the expected length of a perpendicular segment $CA$ (perpendicular over $AB$), how do I calculate the point ...
2answers
722 views

### How to calculate angles and X,Y coordinates for drawing a hand of playing cards on a canvas

Scenario: I'm programming a module to draw a deck of cards on a canvas as though they were being held by a person. Edit: I've cleaned up the question as best I can to be clearer. What I'm looking ...
0answers
567 views

### Direction ratio of a vector in 3d?

Suppose I have a vector whose starting end is the origin & the other end can be in any of the 8 quadrants (in 3d). I can easily get direction ratios for the vector & also know in which ...
3answers
172 views

### Constructing a line with a known line, intersection point and angle.

I am creating a Java game with collisions. I found myself stuck on the following problem. I have got two known lines: $y$ and $i.$ $i$ is the inbound direction and $o$ the outbound direction, ...
1answer
35 views

### Finding unknown 3D vector given 2 known vectors and 2 known angles

So I have a 3D vector math problem that I'm having difficulty solving. Basically I have two known vectors in the form (x,y,z), let's call them C and P, and I want to find a third unknown vector, let's ...
2answers
128 views

### is this equation solvable?

Can someone please solve these 2 equations to get values of h and k? I know the values of h and k but not sure how to solved these equations to get h and k 's values \$(20.01 - h)^2 + (17.94 - k)^2 = ...
3answers
90 views

### calculating a point on circumference

See the diagram Known values are A: (-87.91, 41.98) B: (-104.67, 39.85) C: (-96.29, 40.92) L: 14.63 // L is OC Known angles ...
5answers
1k views

### finding center of circle

How can I calculate center of a circle $x,y$? I have 2 points on the circumference of the circle and the angle between them. The 2 points on the circle are $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$. The ...
4answers
314 views

### Best way to find the Coordinates of a Point on a Line-Segment a specified Distance Away from another Point

I have 4 points: $Q, R, S, T$. I know the following Coordinates for $R$, $T$, and $S$; Length of $\overline{RQ}$ That segment $\overline{RT} < \overline{RQ} < \overline{RS}$; I need to ...
3answers
493 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 + ...
3answers
609 views

### How is the angle between 2 vectors in more than 3 dimensions defined?

I would like to know how the angle between two n-vectors is defined. I mean whether it is unique and how we may compute it (is the inner product a valid method in the n-dimensional space?). I have ...
1answer
162 views

### Trying to find an unknown point just with angles

This is my model: What I do know: A, B, C, which form an equilateral triangle Mab, Mbc, Mac which are the middle points Angles x and y, which are the angles formed by the segment from the unknown ...
3answers
3k views

### Equation of angle bisector, given the equations of two lines in 2D

I have two lines in 2D expressed with general equation (or implicit equation): First line: $a_1x+b_1y=c_1 \qquad(1)$ Second line: $a_2x+b_2y=c_2 \qquad(2)$ If the two lines are intersecting I will ...
3answers
2k views

### Finding point coordinates of a perpendicular bisector

Given that I know the point coordinates of A and B on segment AB and the expected length of a perpendicular segment CD crossing the middle of AB, how do I calculate the point coordinates of segment ...
3answers
2k views

### Find the coordinates in an isosceles triangle

Given: A = (0,0) B = (0,-10) AB = AC Using the angle between AB and AC, how are the coordinates at C calculated?
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9230014681816101, "perplexity_flag": "middle"}