Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.
2
votes
3answers
96 views
Fractional Trigonometric Integrands
$$∫\frac{a\sin x+b\cos x+c}{d\sin x+e\cos x+f}dx$$
$$∫\frac{a\sin x+b\cos x}{c\sin x+d\cos x}dx$$
$$∫\frac{dx}{a\sin x+\cos x}$$
What are the relations between the numerator in the denominator, and ...
3
votes
2answers
140 views
How to find the solutions $x$ of $ 2\sin{11^{\circ}}\sin{71^{\circ}}\sin{(x^{\circ}+30^{\circ})}=\sin{2013^{\circ}}\sin{210^{\circ}}$
Let
$$2\sin{11^{\circ}}\sin{71^{\circ}}\sin{(x^{\circ}+30^{\circ})}=\sin{2013^{\circ}}\sin{210^{\circ}}$$
where $90^{\circ}<x<180^{\circ}$.
My idea: ...
0
votes
1answer
18 views
What is Angle(A,b) about something.
I was reading a paper and came through a notation saying ....
Angle = Angle(A,B) about C.
Can anybody tell me what exactly it means.
Thnaks,
Harsha
0
votes
1answer
25 views
Need “up” vector to calculate distance from a focal plane given world coordinates (SOLVED)
I have a RGB image, and for each pixel in the image I also have its real world coordinate. I also have the location (real world coordinate) yaw, pitch and roll of the camera. I am trying to produce ...
0
votes
2answers
83 views
Trapezoid rule over trigonometric polynomials
The question is regarding trapezoid rule applied on trigonometric polynomials
Here is the question
Show that the composite trapezoid rule over an equidistant partitioning with interval size $h = ...
0
votes
3answers
63 views
Differentiate $y = {(x + 2)^3}{(1 - \sin 2x)^2}{(1 + \tan x)^3}$
I haven't got very far in attempting this:
$\eqalign{
& y = {(x + 2)^3}{(1 - \sin 2x)^2}{(1 + \tan x)^3} \cr
& y = {\left( {(x + 2)(1 + \tan x)} \right)^3}{(1 - \sin 2x)^2} \cr} $
I'm ...
9
votes
2answers
175 views
Inequality $\sum_{1\le k\le n}\frac{\sin kx}{k}\ge 0$
Show the following inequality for any $x\in [0, \pi]$ and $n\in \mathbb{N}^*$,
$$
\sum_{1\le k\le n}\frac{\sin kx}{k}\ge 0.
$$
I have this question a very long time ago from a book or magazine but I ...
0
votes
1answer
24 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
33 views
How to get to these steps?
I found this question here (I reccomend that you read the question and the highest-voted answer there) How to solve for $x$ in $x(x^3+\sin x \cos x)-\sin^2 x =0$? and the math below is an answer. I ...
1
vote
4answers
84 views
$\lim_{x\to 0} x^3/\tan^3(2x)$
$$\lim_{x\to 0}\frac{x^3}{\tan^3(2x)} $$
My textbook has an answering of $\frac{1}{8}$ and I'm quite confused on how they got that. Only thing that I could see to get an $8$ would be $2^3$ from ...
1
vote
1answer
35 views
Calculating circle properties.
How can I incrementally calculate the angle from angle 0 and the point (x, y) in a circumference path if I have the center of the circle coordinates and the radius of the circle.
I have 127 segments ...
1
vote
1answer
34 views
Prove trigonometric inequality
Could anyone help me prove the following inequality for $x>0$$$x(2+\cos x)>3\sin x$$
If you could just show me the first few steps, that would be great.
2
votes
2answers
47 views
Simplifying $\prod_{k=0}^n \cos(2^{-k})$
A student of mine has trouble with the following, and so do I. The solution should be easy since it has been ask to première S students (equivalent to American 11th grade I guess).
The question is ...
4
votes
0answers
47 views
How to find the maximum diagonal length inside a dodecahedron
I am trying to find the maximum length of a diagonal inside a dodecahedron with a side length of 2.319914107*10^89 meters. I am not sure if any other information than that is needed, if it is I ...
5
votes
2answers
129 views
Could we show $1-(x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}-\dots)^2=(1-\dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dots)^2$ if we didn't know about Taylor Expansion?
Suppose that humanity haven't discovered Taylor Series Expansion of trigonometric functions or of any function that would help us on this. Which means we are not allowed to replace the given infinite ...
0
votes
1answer
78 views
Triangular Inequality
Let a, b, c be the three side lengths of a triangle. Prove that
$$\frac{a}{b+c-a}+\frac{b}{a+c-b}+\frac{c}{a+b-c}\geq 3$$
Under what conditions is equality obtained?
1
vote
2answers
72 views
How do you solve $z^4 = 2(1+i\sqrt{3})$
Solve $z^4 = 2(1+i\sqrt{3})$ in the form $r(\cos\alpha+i\sin\alpha)$ where $r>0$ and $0\le\alpha<2\pi$
I know you have to find $\arctan(\frac{\sqrt{3}}{1})=\frac{\pi}{3}$ and that is $\alpha$? ...
0
votes
1answer
56 views
Euclidean triangle. Does this one exist
Does $\exists$ a Euclidean triangle $ABC$ with $\sin(A) : \sin(B) : \sin(C) = \frac{1}{4} : \frac{1}{3} : \frac{1}{2}$?
1
vote
1answer
82 views
Time Average of Cosine squared function
I've carried out the steps for the time average for $\cos^2x$ for limits $0$ to $T$.
I've gotten : $\frac{1}{T}\left[\frac{1}{2}[T+\frac{1}{4}\sin2T\right]$
I'm trying to find the average over a ...
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 ...
0
votes
1answer
69 views
0
votes
0answers
13 views
Is there a formula to get the changes in ship course from wind and current?
Anyone know how to get the changes of degree's in ship course that affected by wind and current?
I thinks it maybe related with the speed and degree of WIND and CURRENT. But I don't know how to ...
0
votes
2answers
27 views
Turning points on $2\sin x - x$
I'm self teaching and doing a book exercise which asks: "Considering only positive values of x, locate the first two turning points on the curve $2\sin x - x$ and determine whether they are maximum or ...
5
votes
3answers
83 views
Simplifying $\sin(2\tan^{-1} x)$
I've been working on this for a while. The answer in the book is $\frac{2x}{x^2 + 1}$ Here's my workings:
$\sin(2\tan^{-1} x)$
Let $\alpha = \tan^{-1}x \Rightarrow \tan \alpha = x$
$\sin(2\alpha) = ...
4
votes
1answer
65 views
How can I calculate the angle of a slice of an ellipse?
I'm attempting to draw a pie-chart programmatically, using an ellipse instead of a circle, but I'm having trouble calculating the correct angles for the slices. If it were a circle, I could use the ...
3
votes
1answer
64 views
Find the maximum value of $T=\frac{2}{3}(\cos 2A-\cos 2B)-\tan\frac{C}{2}$
Let $ABC$ be a triangle. Find the maximum value of
$$T=\frac{2}{3}(\cos 2A-\cos 2B)-\tan\frac{C}{2}$$
Please give me some hints. I don't know where to start
Thanks
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 .
7
votes
3answers
189 views
Broken Calculator: only certain unary functions work.
I have run into a challenge on Codecademy.com that has me absolutely bewildered. I'm sure I'm just overlooking an obvious solution, but I've been scouring tables of trigonometric and logarithmic ...
1
vote
2answers
45 views
Proving that $\frac {\cos(π + x)\cos(-x)}{\cos(π-x)(\frac{π}{2}+x)} = \cot^2(x)$
Prove:
$$\frac {\cos(\pi + x)\cos(-x)}{\cos(\pi - x)\cos(\frac{\pi}{2}+x)} = \cot^2(x)$$
I tried to solve the left hand side but got the answer as $-\cot(x)$ instead.
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
0answers
35 views
Geometry question
The sides of a triangle are given to be $x^2+x+1$ , $2x+1$ and $x^2-1$. Then the largest of the three angles of the triangle is
a)75 degree
b)$\dfrac{x}{x+\pi}$
c)120 degree
d)135 degree
please ...
0
votes
1answer
44 views
Prove that $x^r$ with $r=a+ib$ or $r=a-ib$ defines real solutions
Prove that $x^r$ with $r=a+ib$ or $r=a-ib$ defines real solutions in terms of trigonometric functions with argument $\ln x$ multiplied by exponential function $y(x)=x^{(a+ib)x}$ or
$y(x)=x^{(a-ib)x}$
...
1
vote
1answer
29 views
Simple trigonometry simplification
$\dfrac{(1-\sec^4\theta)(1-\sin^4\theta)}{\sin^2\theta-2}$
When simplifying the expressions above, how can I eliminate the denominator?
I have tried expanding the nominators by ...
1
vote
3answers
36 views
Pythagoras/trigonometry question
Does anyone know how to answer this question?
A right-angled triangle is to be constructed with hypotenuse (the longest side) of length
one metre in such a way as to maximize the perimeter of the ...
0
votes
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!
$$\sin \theta = A_{1} \cdot ...
0
votes
1answer
25 views
Can I find the magnetic heading from A to B on triangle ABC if the lengths and angles inside the triangle are known?
I want to find the magnetic heading (from north) from a point $A$ to a point $B$ on a $\triangle ABC$. $A, B and C$ are moving and so the angles can be any value. as an example, the triangle could be ...
1
vote
1answer
48 views
How do I determine a formula for a given trig function?
Assume that 0 < x < pi/2 and sin(x) = z
a.) Find a formula that gives the value of sin(x/2) in terms of z
b.) Corroborate the validity of the formula for these values of x:
pi/4
pi/3
pi/6
...
4
votes
1answer
90 views
How to calculate distance on a sphere with an earth like coordination system?
This is probably a too simple question for this site, but I would really appreciate any answers.
Lets say I've got a sphere with radius $r = 70$ meters. This sphere has an Earth-like reference system ...
2
votes
2answers
76 views
A trigonometric proof
How to prove the following?
$${1-\sin A \over1+\sin A} = (\sec A- \tan A)^2$$
this is what I've done till now:
\begin{array}{ccc}
{1-\sin A \over1+\sin A} &=& {1+\sin^2 A - 2\sin A \over ...
1
vote
3answers
22 views
Mean value theorem proof with tangent
I am trying to show that:
$\tan{x}>x$ for $0<x<\pi/2$.
How can I show this? I think I can do something with the fcn $\tan{x}-x$ and it derivative, but how can I use this in a proof?
...
0
votes
1answer
39 views
Finding a function which fits this data?
I need to find a polynomial (or other continuous elementary function) on the interval [70, 180] such that it passes through the points (70, 0) (this is a relative min), (105, 17) (this is a relative ...
0
votes
3answers
27 views
steps for finding inverse tangent
My textbook gives me this:
Can someone please walk me through the steps to get -pi/3 from the inverse tangent?
1
vote
1answer
42 views
Adding integer multiples of pi
I have an angle with a given radian measurement and need to express it differently by adding integer multiples of pi. Is it accurate to say that I can simply add 4 to the coefficient of pi? It seems ...
0
votes
1answer
17 views
How can I solve an equation based off of a quadrant and equation form given an angle?
Given that 3pi/2 < z < 2pi
x = arccos(sin(z))
Given different values for z (which are angles on the unit circle) how would I write the results in these two forms, where C is a constant?:
a.) ...
2
votes
1answer
58 views
Getting an acute angle for an obtuse angle using law of Sines.
I have done this problem over and over again. I even looked up tutorials on how to properly use law of sines. It's rather embarrassing that I'm struggling so much wish this simple trigonometric stuff.
...
2
votes
2answers
68 views
Finding ALL solutions to $2(\sin^2(x)) - 5\sin(x)-3 = 0$?
What does it mean to find "ALL possible solutions?"
I know it has something to do with simplifying the equation, getting the angle (in radians) by doing the inverse.. and adding $2\pi n$?
So given ...
0
votes
1answer
35 views
Did I solve all of the steps of this Trig question properly?
Thanks to some help from the community, I think I did this problem correctly, but I would like someone to confirm that I indeed do it right. Thanks.
Question:
Let $0 \le x \le 1$.
(i.) Find the ...
1
vote
2answers
37 views
How do I write a trig function that includes inverses in terms of another variable?
It's been awhile since I've used trig and I feel stupid asking this question lol but here goes:
Given:
$z = \tan(\arcsin(x))$
Question:
How do I write something like that in terms of $x$?
Thanks! ...
3
votes
1answer
24 views
Using a particular image to justify a (specific) trig integral equality.
I would like to include the following string of equalities in a paper:
$$\sin ^2(x) + \cos ^2(x) = 1$$
$$\int _0^{\dfrac{\pi}{2}} \sin ^2 (x)dx + \int_0^{\dfrac{\pi}{2}} \cos ^2 (x)dx = ...
1
vote
0answers
47 views
How can I find the compact trigonometric Fourier series from these signals?
I've been stuck on this for a while, but how exactly would I go about calculating the compact trigonometric Fourier series for both of these signals? I have a general formula down for it, but I just ...
