# Tagged Questions

3answers
91 views

### Moments at which moving points on a circle coincide

Points A $(0,1)$ and B $(1,0)$ start moving along the circumference of a unit circle with center $(0,0)$ in the same, positive (that is, counterclockwise) direction. Every minute, points A and B ...
1answer
41 views

### Check my solution to this trig inequality

Problem $1.88$ : Solve $$\cos x\lt \frac{\sqrt{3}}{2},\qquad x \in [0,2\pi]$$ I found the set of solutions to be $S=[0,2\pi]-\left[\dfrac{\pi}{6},\dfrac{11\pi}{6}\right]$ Is this correct? Thank you.
3answers
27 views

### solving for the left side for a double angle formula

$\cos t-\sin 2t=0$ Solve the left hand side so that it equals zero. Do I use $(2\sin t \cos {t})$ for $\sin 2t$?
3answers
81 views

### Trigonometry, knowing 3 sides how to find the height?

I have a mathematician problem where, I knew the 3 sides of a triangle, with these sides I can figer out what type of type of triangle is. What I realy want to find is the height of the triangle and ...
1answer
18 views

### Concept of parallelism in analytic terms

Below I cited a passage from Apostol's Calculus. I don't understand how to use the identity to show that two lines with equal slopes are parallel. Concepts such as perpendicularity and parallelism ...
2answers
41 views

### This question on right triangles. [closed]

a ladder 10 ft. in length is leaning against a wall 8 ft. above the ground. a 6ft. guy tries pass underneath the ladder 1 ft. away from the wall. will he be able to pass underneath the ladder.
0answers
83 views

### How to calculate center coordinates of two reverse arcs in 3D space

Given 3D points P1(200,60,140), P2(300,120,110), P3(3,0,-1), P4(-100,0,-1) and the radius of arc C1MP3 is equal to radius of arc C2MP1. How do I calculate coordinates x, y, z of points C1 and C2? ...
1answer
67 views

### translate coordinates on circle to percentage?

I'm coming more from a programming point of view but the question is pure math. The only strange thing, I guess, is that the coordinate system is like this: ...
0answers
30 views

### Help solving a function

I have $2$ equations and $2$ angels that i need $V_{1}$ and $V_{2}$. I know The Point $(X_{m}, Y_{m})$ and the point $(X_{a}, Y_{a})$. I have one point $(X_{p}, Y_{p})$ that moves with the equation ...
3answers
145 views

### Proof of Aristarchus' Inequality

Does anyone know how to prove that if $0<\alpha<\beta<\frac{\pi}{2}$ then $\frac{\sin\alpha}{\alpha}>\frac{\sin\beta}{\beta}$. Any methods/techniques may be used.
1answer
1k views

### Proof of vector addition formula

Two vectors of lengths $a$ and $b$ make an angle $\theta$ with each other when placed tail to tail. Show that the magnitude of their resultant is : $$r = \sqrt{ a^2 + b^2 +2ab\cos(\theta)}.$$ I ...
1answer
347 views

### find the rate of change of the area of triangle pulled by three people from its sides

this is the problem of my curious mind(I am it's designer!) . three people each having the rope attached by the end of the 3 sides of triangle ABC , pull the triangle with speed U in the direction ...
2answers
87 views

### How to find $P_1$ in $(x,y)$ form

From following diagram, $A_1$ is center of circle of radius $r$. All distances are in coordinate system $(x,y)$. Distance from $A_1P_2$ is known. Distance $A_1,A_2,A_3$ is also known from origin. I ...
0answers
82 views

3answers
2k 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
239 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
7k 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
3k 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
3k 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?