3
votes
2answers
54 views

Calculation for the chance of finding something a given distance from a starting point by walking straight in a random direction?

The premise is basically a 2D plane with a single point, the starting point. Now a landmark sought by a hiker is a certain distance from that point. If the hiker can only see 1 mile in any ...
2
votes
2answers
50 views

Different Definitions Of The Sine Function

I was hoping someone could give me a flow chart or high-level map connecting all of the definitions of the sine function, with some of the reasons why we care next to each. I've tried this but I'm not ...
1
vote
2answers
31 views

The bird pointer problem: finding the angle of rotation

Suppose we have a bird pointer. He is a guy that likes to point at birds in the sky: His legs cannot move, however he can rotate around his torso. Also, his body and his arm always make a right ...
0
votes
1answer
21 views

Conversion of angle from 360 degree to-90 degree

Here i am trying to convert angle into +90 degree AND -90 DEGREE FORMAT.For desired elevation angle i got answer properly.How to converert angle -90deg to zero, zero to +90 degree format. you can ...
-2
votes
0answers
38 views

Trigonometry-how to do? [closed]

AB (3m) is an advertisement board perched on pole BC. CD is a horizontal ground level. AD=12m and BD=10m. Find the length of elevation of A from D and B from D. Find the length of BC.
1
vote
2answers
31 views

Thinking of sohcahtoa with 90 in a triangle.

I know the answers from a unit circle. But when looking at a triangle how do you interpret Angle C sin C = cos C = tan C = I know the cos 90 = 0 and ...
21
votes
5answers
4k views

Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small?

I haven't touched Physics and Math (especially continuous Math) for a long time, so please bear with me. In essence, I'm going over a few Physics lectures, one which tries to calculate the Force ...
1
vote
1answer
32 views

Solving right triangle given the area and one angle

Given right angle triangle $ACB$ (C is the right angle) has an area of 224 $mm^2$, what is the length of leg b if angle A equals 31.7deg? Here's the scenario: I have one right triangle completely ...
0
votes
0answers
28 views

Similar triangle, Quick question (Thick Lens Formula)

http://www.panohelp.com/thinlensformula.html On the right hand side, f is defined as focus of the lens, i understand why the image distance is (f + fm). However i have spent an afternoon and could ...
2
votes
2answers
37 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
0
votes
2answers
12 views

A cycloid that goes through the beginning and through a general point

Parametric equations of the general cycloid through the beginning $(0,0)$ are $$x(t)=\frac{2t-\sin2t}{2d}$$ $$y(t)=\frac{1-\cos 2t}{2d}$$ How can we determine $d$ such that the cycloid goes through ...
0
votes
0answers
26 views

Find the relation the 'maps' 2D points to the corresponding 3D images.

I have this [on hold] question (#857264) re-phrased. Hope that the content is more meaningful now. The following is the picture modified from the original. The question is a rectangular piece of ...
1
vote
1answer
25 views

Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
0
votes
1answer
30 views

How to normalize a slope?

Say I have two slopes and two averages for a sample: $m=4{,}000$ dollars/day, average $a=50{,}000$ $n=80{,}000$ dollars/day, average $b=700{,}000$ Graphically, $n$ is very ‘steep’ compared to $m$. ...
1
vote
1answer
47 views

If $ (A_1A_2)^2 + (A_1A_3)^2… + (A_1A_n)^2= 14r^2$, then prove that the number of sides is 7.

Let $A_1, A_2,\ldots,A_n$ be the vertices of a regular $n$ sided polygon inscribed in a circle of radius r. If $ (A_1A_2)^2 + (A_1A_3)^2+\ldots + (A_1A_n)^2= 14r^2$, then prove that the number of ...
0
votes
0answers
33 views

what does secant equal 2 mean? [duplicate]

I need your help, I am a little confused. My question is, what does the value of secant mean? I asked this question previously but unfortunately I did not understand the answers so I am trying to ...
0
votes
0answers
25 views

Vector Magnitude during rotation

Probably something I should now already but this is confusing me no end! Lets say we have a force which is directed at 69 degrees inclination (from the X axis) with a magnitude of 500, shown below: ...
0
votes
2answers
33 views

Circle area and lim

I was trying to show how to find $\pi$ value from formula $\pi R^2$, but I dont understand where is my mistake. So i am calculating area using $n$ triangles 1 let $R=1$, then one triangle area is ...
2
votes
3answers
67 views

Finding an area of a triangle inside of a triangle, given certain areas of other triangles, and area ratios.

I'm studying for the Waterloo Math Contest (Galois, Gr. 10) taking place in April of 2015 and I am preparing by looking at previous problems and solving them. This is question 4(c) on the 2010 Galois ...
4
votes
1answer
44 views

Points for which $AX^2-BX^2$ is constant

My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 8: Two points, A and B, are given in the plane. Describe the set of points for which $AX^2-BX^2$ is constant. I would ...
4
votes
2answers
50 views

Elementary Trigonometry problem

My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 7: Two points, $A$ and $B$, are given in the plane. Describe the set of points $X$ such that $AX^2+BX^2=AB^2.$ The ...
2
votes
2answers
32 views

Get the angle in a circle using center, radius and one point in a circle.

There is a circle and i know Point1 this is fixed and i know another point Point2 which can be anywhere in the circle. and i want to know the angle which is made at center. Thanks Your help will be ...
0
votes
1answer
27 views

Find points near end point of a line

Any equation to find points near to both start and end points of lines with different slopes. See image. Need P and Q. If Endpoints are named A and B, AP and BQ should be 1 cm
1
vote
1answer
49 views

Proving Sin Cos Tan

I am asked to prove the following: $$\dfrac{1-\cos x}{\sin x}=\dfrac{\sin x}{1+\cos x}=\tan\dfrac x2.$$ Looking at the answer I am not able to see what is going on here: $$\frac{1 - ...
0
votes
1answer
22 views

Bounding box of a thick line with end caps

I have been pulling my hair out on the trigonometry on this and just can't seem to get it right. Basically, I need to calculate the bounding box of a line going from point (x1,y1) to (x2,y2) where ...
1
vote
2answers
25 views

Find length of $CD$ where $\angle BCA=120^\circ$ and $CD$ is the bisector of $\angle BCA$ meeting $AB$ at $D$

$ABC$ is a triangle with $BC=a,CA=b$ and $\angle BCA=120^\circ$. $CD$ is the bisector of $\angle BCA$ meeting $AB$ at $D$. Then the length of $CD$ is ____ ? A)$\frac{a+b}{4}$ B)$\frac{ab}{a+b}$ ...
0
votes
1answer
15 views

Get a third point (lat, lng) from two given

I have two points as follow (the distance between them is variable): I need to get a third as shown: The two first points change all the time, including the distance between them. My problem: I ...
0
votes
2answers
45 views

Find the circle touching a line

I have been struggling with this (probably easy to solve) geometry problem for a while. What are the coordinates of the centre and the radius of the circle?
0
votes
3answers
50 views

Alternatives to polar coordinates for mapping point onto one dimensional coordinate

I can map a point (x,y) to polar coordinates (angle,length). However, let's say in this (angle, length) pair, "length" doesn't actually interest me, so I can map (x,y) to a one dimensional ...
5
votes
2answers
80 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
0answers
32 views

Weird inequality answer, truncate or round?

When arriving at the final answer for a double inequality question, it appears that my text book has truncated one part and rounded the other. Is there some weird inequality rule that I don't know ...
0
votes
0answers
27 views

Issue with the geometric proof of lim_{x -> 0} sinx/x = 1

When proving $\displaystyle\lim_{\theta \to 0} \frac{\sin\theta}{\theta} =1$, I have been taught to use a sector with radius 1. How rigorous is this proof if we have not considered a radius of any ...
1
vote
1answer
49 views

find the height of the tower

A person standing at a point $A$ finds the angle of elevation of a nearby tower to be $60^{\circ}$. From A, the person walks a distance of $100 ft$ to a point $B$ and then walks again to another point ...
0
votes
1answer
36 views

What is the theorem called that states that equal angles gives equal sides?

We have an isosceles triangle, what is the theorem called that states that the sides opposite it's congruent angles will have congruent lengths? Could someone also explain why this is.
3
votes
2answers
62 views

What is the relationship between the area of a triangle and an area of a segment of a circle?

I had a very smart physics teacher in the past remind us of the area of a segment of circle through this 'derivation': "well, if you put two of those together doesn't it kind of look like a ...
0
votes
0answers
39 views

Find probability of angle being obtuse

We are given points A and B on the 2D plane and distance between them is 2. Let C - randomly picked point on the circle with radius R and center at the middle of AB. Find probability of angle ABC ...
0
votes
1answer
24 views

Inscribed circle: find distance to circumscribing circle

Let a circle with center $b$ and radius $r$ be contained in a circle with center $a$ and radius $R$. Given a point $c$ on the small circle, find its distance to the greater circle. That is find the ...
0
votes
0answers
32 views

Is it possible to solve this series of triangles with only the given information?

Consider the following: As displayed in the picture, the distance between the points is 1, so the last point's coordinates would naturally be $(c, d+4)$ Is it possible to solve for the coordinates ...
3
votes
1answer
45 views

Find Area of 3 Sector Circle, Variable center point

I have a Circle separated into 3 sectors. At start each sector has the same central angle, 120°. Therefore each sector should be taking up the same area. I want to be able to move the center point ...
0
votes
0answers
39 views

smaller circle into larger circle : find length of common arc

Let a circle of radius $r$ be contained in a larger circle of radius $R$ such that the two circles touch. What is the length, in radians of the common arc, in blue? I think the solution is ...
1
vote
3answers
92 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 ...
0
votes
0answers
14 views

what triangles have rational ratio in side and angle? [duplicate]

It's the same with the title, what triangles have rational ratio in side and angle? I mean, what triangles have rational ratio among sides and angles?
1
vote
0answers
44 views

Rationality in Triangle

How can I justify this answer? I think the answer is infinite, but cannot justify it///
3
votes
2answers
125 views

Determining the angles of a triangle given the ratio between its edges

Given that a triangle has edges of ratio 2 : 3 : 4, the task is to determine the three angles, say in degrees. I started by drawing 4 cm segment on the paper, then drew perpendicular segments of ...
0
votes
1answer
36 views

Equation of tangent on Cartesian plane given center and radius of a circle

If I have a generic circle with radius $r$ and center $(h, k)$, and a tangent line with point of tangency $(x, y)$, can you give me the equation of the tangent line? Thanks!
2
votes
0answers
49 views

Angular velocity of the minute hand

The exercise is to calculate the angular velocity (in radians per hour) of the rotation of: the hour hand, and the minute hand (of the clock). Neither of my answers coincides with the answers in ...
0
votes
1answer
65 views

How to determine the visibility of an object from the top of a hill

We are developing software to train children how to cross the street safely. Part of the training is to teach them not to cross when they don't have enough visibility due to obstacles. In this case, ...
0
votes
1answer
48 views

Solving for an angle using trigonometry.

Trying again $\dfrac{\sin(180 - \theta - a)}{H + R} = \dfrac{\sin(a)}{R}$ $\dfrac{\sin(\theta + a)}{ H + R} = \dfrac{\sin (a) }{ R}$ (is this correct?) ${\sin(\theta + a)} = \dfrac{{ H + R}}{ ...
0
votes
1answer
16 views

Ordering angles using max and min functions

I'm using the awesome Desmos Graphing calculator to graph cyclic quadrilaterals. The idea is that the user can drag a slider to change the value of the angle of each point A, B, C and D. I have done ...
0
votes
0answers
10 views

Calculus of trigonometric functions based on elliptic Gauss functions?

Considering this 3 concepts: Arithmetic geometric mean Elliptic integral ( in relation to Gauss studies ) Newton's method I'm supposed to be able to write an algorithm to compute trigonometric ...