Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.
4
votes
1answer
90 views
Find area bounded by two unequal chords and an arc in a disc
Math people:
This question is a generalization of the one I posed at Find area bounded by two chords and an arc in a disc . Below is an image of a unit circle with center $O$. $\theta_1, \theta_2 ...
4
votes
1answer
87 views
Is this a valid proof of the derivatives of the trigonometric functions?
For the sake of this proof, the trigonometric functions $\cos$ and $\sin$ are defined as the coordinates of a point on the unit circle, rather than any of the modern analytic definitions.
Let $\vec ...
4
votes
1answer
55 views
Total variation of a Fourier series
Let $f(x) = f(x+2\pi)$ be a bounded real function given by the Fourier series of the form
$$
f(x) = \sum_{k=1}^N a_k \sin(kx + \phi_k).
$$
What is the total variation $V(f)$ of this function over one ...
4
votes
1answer
215 views
How can I compute $\int_{-\infty}^\infty f(x)f(y-x)\, \mathrm dx$
If $f(x)=\text{arccot}(x)$ for non-negative $x$ and $0$ otherwise, how can I calculate
$$\int_{-\infty}^\infty f(x)f(y-x)\, \mathrm dx$$
for $y\in\mathbb{R}$?
3
votes
1answer
51 views
Trigonometry Airplane question. Finding bearing and distance.
A little background(if you don't care for my story, skip straight to the question): I've missed a few lectures from my teacher because I fell ill. Since I have no information to work with other than ...
3
votes
1answer
26 views
Largest Quadrilateral from a Set of Points
I posted the below on StackOverflow but was directed here as this may be more mathematical problem but I was looking to implement an algorithm....
I have a discrete set of points.
From this set of ...
3
votes
1answer
79 views
Trig question, can this be solved?
I was wondering is it possible to solve this without assuming that CAD=DAB. As I use the law of sines, trigonometry and have tried to apply law of cosines. However, I cannot see how you can solve ...
3
votes
1answer
122 views
Does multivariate integral make sense and can it be evaluated?
I have very hard instructor for multivariate calculus. He ask if the next integral is well-defined.
$$ \iint\limits_D\ {\cos(z)\sin^3(z)\cos(y)\sin(y)\over ...
3
votes
1answer
195 views
cyclic polygons & trigonometry
At one vertex of a pentagon inscribed in a circle of unit diameter (unit diameter, not unit radius) let the angles between adjacent diagonals be $\alpha,\beta,\gamma$, at the next, ...
2
votes
1answer
30 views
Trigonometry Word Problem--Not sure if correct
From point $A$ the angle of elevation to the top of a newly constructed building is $17.2$ deg. From point $B$ which is $153$ meters closer to the building the angle of elevation at the top of the ...
2
votes
1answer
31 views
If $\tan ^{ -1 }{ x } =4\tan ^{ -1 }{ y } $, then for which of the following values of $y^2$, $x$ is not finite
If $\tan ^{ -1 }{ x } = 4\tan ^{ -1 }{ y }$, then for which of the
following values of $y^2$, $x$ is not finite
$2+\sqrt{2}$
$3-2\sqrt{2}$
$3+2\sqrt{2}$
$3+4\sqrt{2}$
My ...
2
votes
1answer
63 views
Why is $e^{g(x)} = \pi$ where $g(x)$ is holomorphic in Weierstrass factorization of sine function?
Why is $e^{g(x)} = \pi$ where $g(x)$ is holomorphic in Weierstrass factorization of sine function? I just can't get why it's true.
2
votes
1answer
27 views
How to show that $f(x) = \cos^2(x)\sin(x)$ is symmetric about the line $x=\frac{1}{2} \pi$?
I really have trouble with making any exercises regarding point symmetry and line symmetry. For example:
Show that $f(x) = \cos^2(x)\sin(x)$ is line symmetrical in the line $x=\dfrac{1}{2} \pi$.
...
2
votes
1answer
106 views
Trigonometry - heights and distances
The angle of elevation of a cliff from a fixed point A is $\theta$. After going up a distance of k metres towards the top of the cliff at an angle of $\phi$ it is found that the angle of elevation is ...
2
votes
1answer
90 views
calculated reflected point within circle
The problem to solve is this.
Imagine a circle. We know two points on the circumference, anchor A and anchor B, they could be anywhere on the circumference of the circle. Draw a line between these ...
2
votes
1answer
296 views
Calculate Length in Perspective View
I have a 4-sided plane in a perspective view. Each side is equal in length to the side across from it. Given the length of two sides and the fore-shortened length of one side, how can we solve for the ...
1
vote
1answer
39 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
20 views
Circular motion trig
We have $x_P = -2 + 4 \cos (-\pi t)$ and $y_P = 1 + 4 \sin ( - \pi t)$ with $t$ in seconds.
We have to find the coordinates of the intersection with the y-axis. So I use trig and I eventually end up ...
1
vote
1answer
16 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 ...
1
vote
1answer
60 views
finding Length of a diagonal
Given Quadrilateral ABCD in such that $AB<BC<CD$ creating increasing arithmetic progression with sum of $27$ cm.
$\measuredangle BCD=60^{0}$. the diagonal $BD=\sqrt{133}$ cm, and it divided ...
1
vote
1answer
16 views
Direction and Distance to a line which goes from location A to location B
I have two location specified in latitude and longitude. Between these location is a line (bearing). I am at a third location. How do I determine how far I am away from this line and in what direction ...
1
vote
1answer
19 views
Formula for Damage Calculation Based on Distance
I am working on programming a game, and I want the damage that a player takes to be based off of the distance they are from the explosive. Consider it like a grenade. Right on the blast radius ...
1
vote
1answer
35 views
Trig problem, finding angles and ranges
I have what may well be a simple problem, but it's been too long since I've done this type of problem. From a fixed point (intersection of all the lines), the angles to 3 other fixed points $a,b,c$ ...
1
vote
1answer
184 views
A sufficient condition to ensure $\alpha=\beta$
Let $\alpha$, $\beta$ be acute angles satisfying
$$
\frac{\sin 2\alpha}{\sin(2\alpha+\beta)}=\frac{\sin2\beta}{\sin(2\beta+\alpha)}
$$
Show then $\alpha=\beta$.
1
vote
1answer
30 views
Finding the angle.
first question here.
I ran into a problem where my math skills are just not enough, probably it's simple, but I don't know how to approach it.
I'll show you this graphic so you can understand what I ...
1
vote
1answer
27 views
Determine the central angle theta
Suppose the ends of the cylindrical storage tank in the figure arc circles of radius $3$ ft and the cylinder is $20$ ft long. Determine the volume of the oil in the tank to the nearest cubic foot if ...
1
vote
1answer
60 views
How to rotate base points of a scalene triangle to represent an isosceles triangle
Given the following graph:
Where SP is the start point and EP is the end point of a line - how would I rotate p1 and p2 on axis SP in such a way that they would represent an isosceles triangle e.g.
...
1
vote
1answer
73 views
A “known” tangent half-angle formula?
The equality
$$
\cos\eta+i\sin\eta = \frac{1+\cos\theta+c\cdot i\sin\theta}{1+\cos\theta-c\cdot i\sin\theta} \tag{1}
$$
or equivalently
$$
\frac{1+\cos\eta+\frac1c\cdot ...
1
vote
1answer
85 views
Combined horizontal and vertical rotation angle?
I am a programmer and I am working on a game tool used in a tank-combat simulator. I usually post my questions on StackOverflow, but this one is Math-only, so I'm guessing this site suits it better.
...
1
vote
1answer
79 views
pre calc, sinusoidal equations
If the sea level decreases leaving the seabed exposed (normally $30$ feet below sea level), then it rises a equal distance above sea level. waves have a maximum height of $38.9$ meters. the cycle of ...
1
vote
1answer
229 views
How to plot N points on the surface of a D-dimensional sphere roughly equidistant apart?
Let's say I have a D-dimensional sphere with a radius R. I want to plot N number of points evenly distributed (equidistant apart from each other) on the surface of the sphere. It doesn't matter where ...
1
vote
1answer
39 views
Finding the values of $Q$ from $180^{\circ}$ to $360^{\circ}$
I have $\cos{Q}=-0.5$, required to find $180^{\circ}\leq Q\leq 360^{\circ}$.
What I tried: The acute angle is $60^{\circ}$, then, since cosine is negative on third quadrant, I suppose the value is ...
0
votes
1answer
50 views
Drawing an arc between two points
I was writing a java program to draw an arc.
Arc2D.Double(int x,int y,int width,int height,int startAngle,int arcAngle,int type);
Since, I'm not familiar with the mathematics behind drawing arc, I'm ...
0
votes
1answer
22 views
Calculate points(x, y) within an arc
I am trying to draw lines from the center of a circle to points (x, y) in the circumference.
To calculate this the angle is used. I need to render points in between two angles. E.g. Angle 0 to angle ...
0
votes
1answer
20 views
Coordinates of all 'N' points, equidistant from each other , on a circle of radius 'R' whose center is (h,v) from the origin?
How would I calculate the coordinates of all 'n points' equidistant from each other on a circle of radius r and the center coordinates of (h,v) from the origin .
0
votes
1answer
40 views
How to find a new point on rectangle based on an known point on the same?
I have rotated a rectangle a certain amount of degree and got the point(x,y)=(130,40) which was previously (152,60). Now i want to find the x,y(marked as red) value at another location based on the ...
0
votes
1answer
23 views
Can I find the magnetic heading from A to B on triangle ABC if the lengths and angles inside the triangle are known?
I want to find the magnetic heading (from north) from a point $A$ to a point $B$ on a $\triangle ABC$. $A, B and C$ are moving and so the angles can be any value. as an example, the triangle could be ...
0
votes
1answer
45 views
Find all solutions/zeros
Find all solutions in the interval$ [0,2\pi]$:
1)$3\sec^3x=4\sec x$
2)$2\sin^2x+3\sin x+1=0$
3)$\cos x+\sin x \tan x=0$
4)$2\sec^3x+\sec^2x–8\sec x–4=0$
Thnx so much
0
votes
1answer
35 views
What is required to establish the law of cosines?
In my quantum computation course, we have been given nothing more than the basic axioms of a linear vector space, and and the properties of an inner product; but we have started referring to "the ...
0
votes
1answer
25 views
The law of cosines for a sphere
$\cos(c) = \cos(a)\cos(b) + \sin(a)\sin(b)\cos(C)$
Prove that if $a$, $b$, and $c$ is approximately $0$, then $c^2 = a^2 + b^2 - 2ab~\cos(C)$.
I wasn't sure how to prove this. One thought I had was ...
0
votes
1answer
68 views
How to find the trigonometric identities?
We find many sources on the internet that provides a table of trigonometric identities (like http://www.fis.ufba.br/~luciano.abreu/TABELA.pdf), but I'd like to know if there is a way to determine ...
0
votes
1answer
53 views
How do I verify a three variable identity?
I am confused on how to verify an identity with three variables.
Problem: $$\cos(x+y+z) = \cos(x) \cos(y) \cos(z)$$
Where do I start?
Thanks
0
votes
1answer
49 views
$\tan(x)$ with phase shift and period
I'm trying to transform $$y=A \tan(Bx-C)+D$$ so that there are two consecutive vertical asymptotes at $x=17$ and $x=19$.
I want the period to equal $2$ and so I set $B=\pi/2$. I want a vertical ...
0
votes
1answer
68 views
Calculate all parameters of a triangle from some known partial lengths and angles
I have the problem described in this image (not to scale): http://i.imgur.com/owWVUmj.png
A (partial cathetus), B (small, vertical cathetus) and C (which forms a 90º angle with hypotenuse) are known ...
0
votes
1answer
74 views
Solving trigonometry equations from graphs when transformations (e.g. 3Tan²) are involved?
Preface; I'm not asking for answers (that won't help me learn Maths at all!), but certainly some guidance would be very much appreciated.
I'm trying to solve some trigonometry equations from graphs, ...
0
votes
1answer
88 views
Circle intersection in radial coordinates?
We have two circles in the plane described by $C_0 = (x_0, y_0, r_0)$ and $C_1 = (x_1, y_1, r_1)$
We know that they intersect but one does not completely overlap the other. That is to say their ...
0
votes
1answer
38 views
Diameter of a circle
Suppose that the diameter of a circle has length $d$. The length of a chord is $c$, and the length of the arc cut off by the chord is $s$.
Express $\;\sin\left(\dfrac{s}{d}\right)\;$ in terms of $c$ ...
0
votes
0answers
118 views
How to convert an angle to an isometric angle, and back?
I have a question about isometric.
How can I convert angle 90 to an tilted isometric angle?
Lets say I have a 2D angle 45 deg, how to translate it to isometric. Isometric is lets say 45 deg tilted.
...
0
votes
0answers
174 views
Trig identities for $A\sin^2(x)+\cos^2(x)$
Does anyone know of any useful trig identities for manipulating $A\sin^2(x)+\cos^2(x)$? The only thing I come up with is:
$A\sin^2(x)+\cos^2(x)=\frac{1}{2}(1+A)+\frac{1}{2}(1-A)\cos(2x)$
I'm trying ...
0
votes
0answers
1k views
Compute Altitude and Azimuth using either Quaternions or Rotation Matrix or Roll, Pitch and Yaw component
I am struck with a mathematical problem. I want to convert the iPhone device's attitude information which is available in one of the following forms:
Quaternion
Rotation Matrix
Roll, Pitch and Yaw ...
