1
vote
1answer
20 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.
1
vote
3answers
25 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 $\sin 2t$?
1
vote
3answers
72 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 ...
0
votes
1answer
17 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 ...
-5
votes
2answers
40 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.
1
vote
0answers
63 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? ...
1
vote
1answer
59 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: ...
-7
votes
2answers
93 views

Prove this trigonometry identity [closed]

Prove that $$\cot B=\frac{\tan{A} - \tan B}{1 + \tan A\tan B}.$$
0
votes
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 ...
1
vote
3answers
120 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.
3
votes
1answer
772 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 ...
4
votes
1answer
331 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 ...
2
votes
2answers
86 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 ...
0
votes
0answers
82 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 ...
3
votes
1answer
818 views

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

How can the focal point of a ball lens be found?
1
vote
1answer
119 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 ...
1
vote
1answer
38 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?
1
vote
2answers
507 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 ...
3
votes
2answers
919 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 ...
1
vote
0answers
1k 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 ...
1
vote
3answers
322 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, ...
2
votes
1answer
40 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 ...
0
votes
2answers
135 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 = ...
1
vote
3answers
103 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 ...
2
votes
5answers
2k 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 ...
2
votes
4answers
756 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 ...
3
votes
3answers
957 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 + ...
4
votes
3answers
1k 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 ...
5
votes
1answer
229 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 ...
9
votes
3answers
6k 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 ...
4
votes
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 ...
4
votes
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?