Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

learn more… | top users | synonyms (1)

1
vote
0answers
34 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 ...
1
vote
0answers
62 views

How to find Latitudes and Longitudes of projections of the vertices of a rectangular plane below earth's surface?

I want to find out the latitudes and longitudes of projections of the vertices of a rectangular plane inside the earth's surface. I know dimensions of rectangle, angles of orientation and latitude and ...
1
vote
0answers
48 views

Rationality in Triangle

How can I justify this answer? I think the answer is infinite, but cannot justify it///
1
vote
0answers
62 views

Logarithm and “basic” functions.

To express the antiderivatives of $\frac{1}{x}$, we cannot apply the formula $\int x^n dx=\frac{x^{n+1}}{n+1}+C$ and we need to introduce a new function, the logarithm. But how can we prove that ...
1
vote
0answers
48 views

Why is that there is no tangent law?

We know that, in a triangle ABC, sine law and cosine law are well developed formulas. My questions are:- Why is that there is no tangent law? (If no, just hope that someone can devise one someday.) ...
1
vote
0answers
27 views

A Hard integral in 2-D.

I'm having a trouble integrating (in $\mathbb{R}^2$) the following formula: $$\frac{t}{|B(x,t)|}\int_{B(x,t)} \frac{||y||}{(t-||x-y||^2)^{\frac{1}{2}}} dy $$ where $B(x,t)$ is the ball with center ...
1
vote
0answers
61 views

Solving an equation with $\arccos(x)$ and $\sin(\arccos(x))$

I want to solve this equation, determining y (all others letters are constants) : $$2 \arccos(3+(1.6y-80)/R) - \sin(2\arccos(3+(1.6y-80)/R)) = 2π(1-P)$$ I've try to use some automatic solvers but ...
1
vote
0answers
42 views

What is the number of x-intercepts in this graph of sine?

The function : $y=3-4\sin(2\pi x-3\pi)$ .. how many $x$-intercepts over the interval $[0,2]$? I am confused if they're 3 or 5 because there are 3 $x$-intercepts that are really intercepting ...
1
vote
0answers
70 views

arrange div elements in circle and square

I n number of divs which are arranged in a circle using javascript. Right now i set the dimension of each div to 40*40. Below is what i am able to achieve so far. This is how i find X & Y of each ...
1
vote
0answers
56 views

proving $\tan^{-1}(x)+\tan^{-1}(y) = \pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right)\;,$ when $x>0,y>0,xy>1$

(1) How ca we prove $\displaystyle \tan^{-1}(x)+\tan^{-1}(y) = \pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right)\;,$ when $x>0,y>0,xy>1$ (2) How ca we prove $\displaystyle \tan^{-1}(x)+\tan^{-1}(y) ...
1
vote
0answers
56 views

How to I solve the inverse $(e^x – je^x)/(e^x+e^x)$?

I have tried using this method https://www.youtube.com/watch?v=V-LJWfuoCDs. But I am getting zero on one side thus cancelling $e^x$, which means that the the answer I get will not be in form of ln. Is ...
1
vote
0answers
44 views

Relation between $\sin(t)$($\cos(t)$) and $\sin(at)$ ($\cos(at)$) when both are rational

This question relates to Parametric equations where sin(t) and cos(t) must be rational. Suppose it is given that $\cos(t)$ and $\sin(t)$ are both rational and also $\cos(at)$ and $\sin(at)$, where ...
1
vote
0answers
37 views

$\cos(2\arccos(\frac{a}{a+1})x$

I have trying to prove that this cosine map: $$\frac{r}{4}((a+1)\cos\left(2\arccos\left(\frac{a}{a+1}\right)\ \left(X_n-\frac12\right)-a\right)$$ is a logistic map. What I have done so far: Using ...
1
vote
0answers
36 views

A right triangle with sides

Imagine a right triangle with sides: Long side C is $4n$, sides $b$ and $a$ are $2n$ and $n$, where $n$ is an integer. How many right triangles are of this form? My attempt: $$16n^2 = 4n^2 + n^2$$ ...
1
vote
0answers
35 views

Finding the inverse of trig functions

I'm supposed to find the inverse of $$f(x) = \cos(x)+x$$ I usually just substitute $x$ for $y$ and then re-arrange. What do I do in this scenario?
1
vote
0answers
101 views

Formula for nth derivative of $\arcsin^k(x/2)$

I need to find formula for $n$-th derivative of $\arcsin^k(\frac{x}{2})$. I have found formula for ...
1
vote
0answers
38 views

Multiple Waves all in phase (Wave packets)

Suppose there are seven waves of slightly different wavelengths and amplitudes and we superimpose them (textbook is talking about wave packets). The wavelengths range from $\lambda _9 = 1/9$ to ...
1
vote
0answers
158 views

Shadow angle calculation for solar tracking application

Shadow Length Dear all, *I am looking for relationship Between Lmin and solar radiation angle.I know Here in above link they provided relation. But i don't know how to calculate it. x- modules ...
1
vote
0answers
25 views

Trigonometry integration with a bound

So, I want to integrate $\int_\gamma sinz\; dz$ where $\gamma$ is any curve joining $i\to \pi$. Can I say that it is beacause $\int sinz=-cosz$, and $-cosz$ is analytic on the domain containing ...
1
vote
0answers
23 views

Rotating two objects

I have two lines. Both created in this format: Line 1 $$line1 = \left\{ \begin{array}{c} startX, startY \\ endX, endY \end{array} \right\}$$ $$line2 = \left\{ \begin{array}{c} startX, startY \\ endX, ...
1
vote
0answers
61 views

what does the sine function tell you about an input

Intuitively, I'm trying to understand the significance of the input in a sine function. I'm currently, trying to develop intuition behind sinusoids and what the input tells you about the output and ...
1
vote
0answers
17 views

A method of calculation coordinates in order to implement it to a code language!

lets say that we have three points A(xa,ya,za), B(xb,yb,zv), C(xc,yc,zc) with known coordinates in 3d space. Is there a method to calculate the coordinates (x,y,z) of another point D for which the ...
1
vote
0answers
26 views

Calculate the following expression

Calculate the value of $\sin a+\cos a$, knowing that $\sin a\cos a=0.48$ and $a$ belongs to $\left[\pi; \frac{3\pi}{2}\right]$? What I did is: $$\sin a \cos a=0.48\ \ |\times 2$$ $$\sin 2a=0.96$$ ...
1
vote
0answers
58 views

Exact arctan value. Can't be solved ??

I am kind of stuck here. I need to know the exact value of $$ \arctan\left(\sqrt{2} \over 4\right). $$ I am looking into double angle formula's, half angle formulas but honestly, I can't find it? Is ...
1
vote
0answers
34 views

Which figure provides the greatest change in angle per change in distance? (trigonometry)

I have been having a lively discussion with others about the following: We (myself and others) are using triangulation to measure distance to an object with a linear image sensor (CCD) and a ...
1
vote
0answers
48 views

Determining the location of a point in a triangle under the given constraints

ABC is a triangle with AC = 1, AB = c/b and BC = a/b. Q is a variable point on AC such that CQ = x and QA = 1 – x. The perpendiculars from A and C to BQ (extended if necessary) are $d_2$ and $d_1$ ...
1
vote
0answers
42 views

Ratios of right triangle integer multiples to PI

It is known that in a right triangle with angles 30 and 60 degrees the cathetus at the 60 angle is equal to the 0.5 of hypotenuse. In other words an angle with cosine 0.5 is equal to PI/3. Is there ...
1
vote
0answers
65 views

independent/dependent values at different frequencies and phases

I am curious about the following problem. I would like to ask for help solving it. Consider the following $m$ sinusoidal functions $\sin(\omega_{1}⋅t+\phi_1),\sin(\omega_{2}⋅t+\phi_2),..., ...
1
vote
0answers
79 views

The distance between two distinct points in the upper half plane

I'm trying to derive the distance between two distinct points in hyperbolic space and I'm working on the upper half plane. So, with the parametrization $\sigma(t): x=r\cos(t), y=r\sin(t),\; ...
1
vote
0answers
73 views

Area of a triangle using vectors

I have to find the area of a triangle whose vertices have coordinates O$(0,0,0)$, A$(1,-5,-7)$ and B$(10,10,5)$ I thought that perhaps I should use the dot product to find the angle between the ...
1
vote
0answers
277 views

3D Game: Pitch Yaw Roll of a point

I have a flat elliptical plane and I'm trying to figure out how to represent it based on its direction. So I basically need to calculate its pitch, yaw, and roll. I have a camera at $C$, and a point ...
1
vote
0answers
62 views

An other tricky one. Tigonometric integral.

How should I attack this ? $$ \int_0^{\pi} \cos(ax)^m \cos(x)^n dx$$
1
vote
0answers
31 views

Question on trigonometry (acute angle case)

Here is the question of "MOSP (The Mathematical Olympiad Summer Program) $2000$", and it takes me so much time to solve, but I can't. Let $ABC$ be an acute-angle triangle. The question is to prove ...
1
vote
0answers
78 views

$3$ equations - > $2$ unknowns and also trigonometry

I have a big problem with solving this one - I have $3$ equations, and need to find $2$ unknowns: $$\cos(-55.82) = (0.6893\cos(-70) + 0.3381\sin(-70)) \cdot (\cos b\sin c_1 + \sin b\cos c_1) - ...
1
vote
0answers
65 views

How long will it take me to learn math as a beginner

am 18 years old. I won't like to say i don't know maths, but i have a very poor foundation in maths. I am very weak in maths, even some 8 year olds are better than me. I can answer about 4 out of 20 ...
1
vote
0answers
108 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
0answers
203 views

Solving system if equations containing trigonometric functions with Ti-Nspire

In trying to solve the following system of equation: $20000\times9.81+a\cos b=0$ $a\sin b=6.17\times20000$ Find $a$ and $b$ . It gives me something containing "n2" in bold and I don't know why? ...
1
vote
0answers
56 views

Find angle inside of isosceles triangle

The figure explains it best. http://imgur.com/V9tX22Z We have $ABC$ isosceles triangle. We know a few angles as follows: $ACB = 20°$ $PAB = 50°$ $ABQ = 60°$ Find $BQP$ angle
1
vote
0answers
62 views

Law of Cosines Manipulation

I'm supposed to use law of cosines on $S_1S_2P$ in the following diagram: To arrive at the following equation: $$ \frac{r_2}{r_1} = [1 - 2(\frac{a}{r_1})sin(\theta) + ...
1
vote
0answers
40 views

Solving a System of Equations with Cosine

How do I solve a system of equations when there is a cosine. Here is the system: $$ \left\{ \begin{array}{c} a+b=77° \\ \cos(a)=\frac{y}{3.5} \\ \cos(a)=\frac{y+1}{3.5+x} \\ ...
1
vote
0answers
194 views

Definite integral involving exponential, powers and trigonometric functions

Is it possible to evaluate the following integral? $$ \int_{-\pi}^{\pi} e^{-qx^{ak}(x^2+d^2+2 \, dx \cos[t])^{-a/2}} dt $$ I am not able to find any related formula. Note that this integral follows ...
1
vote
0answers
121 views

Definite integral involving powers and trigonometric functions

Is it possible to evaluate the following integral? $$ \int_{-\pi}^{\pi} {m \over m + x^{ak}\left[\,x^{2} + d^{2} + 2dx\cos\left(t\right)\,\right]^{-a/2}} \,{\rm d}t $$ I am not able to find any ...
1
vote
0answers
49 views

Derivative of trig function

Find the second derivative of $ \arcsin(2x^3) $ The solution says for the first derivative : $ \dfrac{1}{\sqrt{1-(2x^3)^2}} \cdot 6x^2 = \dfrac{6x^2}{\sqrt{1-4x^6}} $ When i answered the first ...
1
vote
0answers
662 views

trig help please. finding angle measures

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a radius of 7 inches. Part 1: What is the angle measure, in degrees and ...
1
vote
0answers
40 views

Trigonometry problem gives a wrong answer

A. Find the BC. Information: <) BAC = 65 (the base), AD = 10 I could not get it to work. What I did is, I took ADB and then I divided ...
1
vote
0answers
153 views

Problems with Circles and Lines on a Cartesian Plane

(a) Find the equations of the two circles each of which touches both coordinate axes and passes through the point $(9,2)$. (b) Find the coordinates of the second point of intersection of the two ...
1
vote
0answers
235 views

How to solve a hard trigonometric equation

I have come across a trigonometric equation which I need to solve, $(B+2A\cos(2x+\theta))(2\sin x|\cos (2x+\theta)|-\cos x )+2A\sin x \sin(2x+\theta)|\sin(2x+\theta)|=0 $ $A,B$ and $\theta$ are ...
1
vote
0answers
53 views

Relative angles on unknown surface

I'm hoping someone here could help me with a problem I am having. I have an electronic sensor that measures tilt, and I put this sensor on a 10 degree ramp. The problem is that this portable ramp is ...
1
vote
0answers
43 views

maximize $\csc{(\pi b)}\sin{(\pi ab)}+\csc{(\pi (\frac{1}{a}-b))}\sin{(\pi a(\frac{1}{a}-b))}$

Let $x\in [0, \frac{1}{a}]$ for a positive integer $a$. $f(x)=\csc{(\pi x)}\sin{(\pi ax)}=\frac{\sin{(\pi ax)}}{\sin{(\pi x)}}$. When $b\in[0, \frac{1}{2a}]$, I want to prove that $b$ maximizing ...
1
vote
0answers
74 views

Solutions of the equation: $x\cos(\pi y)=y\cos(\pi x)$

I have to find the solutions $y=f(x)$ of the equation: $$x\cos(\pi y)=y\cos(\pi x)$$ in $x\in[0,\frac{1}{2})$. Is it possible to solve it analytically or I should use only numerical methods? Thanks