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
1answer
337 views

Trigonometric interpolation

From http://en.wikipedia.org/wiki/Trigonometric_interpolation trigonometric interpolation can be calculated as follows: Now assume we have 6 data points (0, 0.1), (1, 0.3), (2, 0.4), (5, 0.3), (6, ...
2
votes
3answers
597 views

How can I prove a point is within a triangle, given three other points?

Could someone please explain the formula behind this, and then provide an example of how to do this? Basically I have 4 points, each with a longitude and latitude number. (They make a polygon quad, so ...
1
vote
1answer
46 views

Replacement of $1/\sin^2$ term in volume integral?

Another question from the Warren text, concerning a replacement Warren makes in a triple integral. I'll gladly include more context if asked, but I'll try to include what I feel is necessary here. ...
2
votes
2answers
117 views

How prove this is an equilateral triangle

in $\Delta ABC$,$AB=c,AC=b,BC=a$and such $$ab^2\cos{A}=bc^2\cos{B}=ca^2\cos{C}$$ show that $\Delta ABC$ is an equilateral triangle this problem I have solution,But not nice, and I think this ...
0
votes
1answer
57 views

if $\sin(p)=\frac{8}{17}$, $\cos(p)=\frac{15}{17}$, $\sin(q)=\frac 35$, and $\cos(q)=\frac 45$, find $\cos(p-q)$

If $\sin(p)=\frac{8}{17}$, $\cos(p)=\frac{15}{17}$, $\sin(q)=\frac 35$, and $\cos(q)=\frac 45$, find $\cos(p-q)$Please help me solve the trigonometry problem described above.
1
vote
1answer
753 views

About a function approximating the $\arctan(x)$

I found in a paper this function: $$f(x)=\frac{8x}{3+\sqrt{25+\left(\frac{16x}{\pi}\right)^2}}$$ is a good approximation of the $\arctan(x)$. If we consider the difference function: ...
2
votes
2answers
125 views

Finding common points of $\cos x$ and $(1/2)^x$

This might be easy math for you guys but I'm just not getting it. Question says,graph: $y= \cos x$ $y=(\frac{1}{2})^x$ On the same axis. Easy enough. Next part says, state $4$ points where the ...
3
votes
1answer
1k views

The limit of arccos(x) is the arccos(x) of the limit?

Recently I came across a proof using the apparant fact that $$\lim_{x \rightarrow a} \cos^{-1}(x)=\cos^{-1}(\lim_{x \rightarrow a} x)$$ with justification: because arccos(x) is a continuous function. ...
1
vote
2answers
194 views

Trigonometry? Get the “half” of a triangle from hypotenuse and cathetus

I've only got the following parts of a triangle: Line A to B Line B to C And optionally the Line from A to C if needed? I'm trying to get the point X Now the problem is, i've got absolutly no ...
2
votes
4answers
76 views

Trigonometry question to prove equation

Can someone please explain to me how to prove this: $\sin2\alpha = \frac{2\tan \alpha}{1+\tan^2 \alpha}$ Also: $\alpha \neq (2k + 1)\pi, k \in \mathbb{N}$ Thanks in advance.
3
votes
1answer
169 views

How prove this trigonometric identity

Show that $$\sum_{k=0}^{n-1}\dfrac{\tanh{\left(x\dfrac{1}{n\sin^2{\left(\dfrac{2k+1}{4n}\pi\right)}}\right)}}{1+\dfrac{\tanh^2{x}}{\tan^2{\left(\dfrac{2k+1}{4n}\pi\right)}}}=\tanh{(2nx)}$$ Thank ...
0
votes
1answer
43 views

Get unrotated position of a rectangle.

I'm struggeling with the following problem. I have a rotated rectangular. The following values are known. The size of the rect, the angle the rect is rotated by and the position of point A. The ...
3
votes
1answer
197 views

A Functional Differential Equation

I was having a play with some trig. identities and noticed the following: $\cos{x}=\frac{\sin{2x}}{2\sin{x}}$ Now, $\cos{x} = \frac{d}{dx}\sin{x}$ so I made the following analogous differential ...
0
votes
1answer
1k views

Finding the angles for a certain value of sine, cosine or tangens

I want to solve the following task: Which angle between 0° and 360° has a cosine (or sine, or tangens) of 0.5? Same task, but for an angle between 540° and 720°? I want to solve it without ...
0
votes
1answer
126 views

Give an equation for the circle with radius 5 centered at (0, 0) in the Euclidian plane.

Give an equation for the circle with radius 5 centered at (0, 0) in the Euclidian plane. What is the format the answer should be in? Is this supposed to be a method in code?
3
votes
1answer
233 views

Polygon sine waves

So I came across this picture on Google+ and I wanted to understand further. I created an equation for the second wave, the one with the square. Here it is: $$y=\frac{\sin x}{\cos(\min(x \mod \pi/2, ...
1
vote
2answers
74 views

Dilemma evaluating integral after sinusoidal substitution

To solve the definite integral $$ I = \int_{-a}^{a} \frac{dx}{\pi \sqrt{a^2-x^2}}$$ I used the substitution $x = a \sin \theta$ and tried to solve the integral without its interval definition, ...
1
vote
1answer
53 views

Simpler solution to a geometry problem

In a set of geometry problems, I got this one: If in a triangle $ABC$ with segments $AB=8$, $BC=4$, and $3A+2B=180^{\circ}$, calculate the side $AC$ My solution was Let ...
0
votes
1answer
40 views

Total angle within a closed surface…

So I know that the degrees of a triangle add up to 180 degrees. This seems to make sense, on some intuitive level. Now, if you have a closed object constructed of four lines (perhaps most simply a ...
0
votes
3answers
117 views

Find inverse of this function…

$f(x) = \sin(x)-\cos(x)$ I got to this point: $$f^2(x)=1-\sin(2x)$$ But I have no idea what to do next. Please help me, give me a hint :D
3
votes
3answers
350 views

Proving a point inside a triangle is no further away than the longest side divided by $\sqrt{3}$

Problem: In a triangle $T$ , all the angles are less than 90 degrees, and the longest side has length $s$. Show that for every point $p$ in $T$ we can pick a corner $h$ in $T$ such that the ...
3
votes
1answer
544 views

Integrating $\cos^3 (x) \, dx$

I am wondering whether I integrated the following correctly. $\int \cos^3 x \, dx$ I did $\int \cos(x)(1-\sin^{2}x)\,dx$ $\int \cos(x)-\sin^{2}x \cos x\,dx$ $\sin(x)-\frac{u^{3}}{3} + x$, ...
1
vote
1answer
31 views

Integration of a trig function

How would the following trig function be integrated. $$\int \cot^{2}x\csc^{2}x$$ I did $$\int(\csc^{2}x-1)\csc^{2}x$$ But I am not sure what to do next.
0
votes
2answers
141 views

Determine if a point lies between two others on an arc parameterization without trig operations

Suppose we are given the points $\{u, v, w\}$ on an arc. The arc starts at $u$ in the direction indicated by the blue vector, and terminates once it has reached all three points. We also know the ...
4
votes
4answers
128 views

Trigonometric problem using basic trigonometry

If $x$ is a solution of the equation: $$\tan^3 x = \cos^2 x - \sin^2 x$$ Then what is the value of $\tan^2 x$? This is the problem you are supposed to do it just with highschool trigonometry , ...
1
vote
1answer
349 views

Fixed-Point Iteration method unable to converge to any of a function's infinte roots

An equation is given to me which has to be solved by direct iteration method: $$sin(x) = {x+1 \over x-1}$$ or $$f(x)=\sin(x)-{x+1 \over x-1} = 0$$ I follow the following procedure with reasons ...
1
vote
1answer
207 views

Why $y=2\tan^{-1}\left(\cos(x)+\sin(x)\right)$ solves $\cos(y)+ \sin(y)(\cos(x)+\sin(x))=1$?

I tried to find those points on the sphere, where $$\cos(y)+ \sin(y)\cos(x)+\sin(y)\sin(x)=1.\tag{1}$$ $y=2\pi n$ is trivial but after some fruitless attempts I gave up and I asked Wolfram. He gave ...
0
votes
3answers
495 views

3D Trig Question?

I've been having trouble with this question: David is in a life raft and Anna is in a cabin cruiser searching for him. They are in contact by mobile telephone. David tells Anna that he can see Mt ...
2
votes
1answer
89 views

Trigonometric equation in two ways gives different answer

I have been given the equation $\sin^2 x+ \cos x +1 = 0.$ I tried to solve it in two ways. First, $1 - \cos^2(x) + \cos(x) + 1 = 0,$ $\cos^2(x) - \cos(x) - 2 = 0,$ $\cos x=2$ or $\cos x=-1$ thus ...
2
votes
1answer
93 views

What am I doing wrong in this trigonometry/rate simulation problem?

I'm refreshing on some trig and cannot figure out how to solve this non-realistic word problem simulating a person walking in a circle. A person is located at the point (8,0) at time, t = 0, and ...
3
votes
3answers
219 views

Summation of $\cos A+\cos(A+B)+ \ldots \cos(A+(n-1)B)$

How would I prove the following result? $$\cos A+\cos(A+B)+\ldots +\cos(A+ (n-1)B) = \frac{\sin\left(\frac{nB}{2}\right) \cos\left[A+\frac{(n-1)B}{2}\right]}{\sin \left(\frac{B}{2}\right)}$$
1
vote
1answer
107 views

Agreed upon domain of inverse trig functions

Why do we choose $[-\pi/2,\pi/2]$ as the domain restriction for $\sin(x)$ when determining $\arcsin(x)$, clearly other restrictions are possible, which also yield a 1-1 function (like ...
0
votes
2answers
4k views

Write $\cos(x)$ in terms of $\sin(x)$

Write $\cos(x)$ in terms of $\sin(x)$ if the terminal point $x$ is in quadrant IV. I know $\cos^2(x)$ $= 1-\sin^2(x)$. And I know that cos is positive in quadrant IV. I am guessing that the answer ...
1
vote
1answer
109 views

sum of legs of inscribed right triangle

Consider a right and isoceles triangle ABC inscribed in a circle such as its hypotenuse forms the diameter AB of the circle (the right vertex is thus at the "apex" of the circle). If we procede to an ...
6
votes
2answers
100 views

Coincidental Trigonometric Identity for Two Particular Values

I noticed that $$\sin(a+b)\sin(a-b) = \cos a \cos b\qquad (1)$$ when $$(a,b)=\left(\frac{2\pi}{5},\frac{\pi}{3}\right)$$ Is there an underlying reason for this coincidence? Concretely, I would like ...
1
vote
1answer
1k views

How do you calculate work (KJ) and Power (W) when jogging on a treadmill?

The following is known... The Weight of the Person, The Angle/grade of the Treadmill, The Time that they are on the treadmill, The velocity of the treadmill. How do I calculate Work in Kilojules and ...
3
votes
1answer
126 views

Largest scaled rotated rectangle inside rectangle

There are two rectangles: $r_1$ and $r_2$. $r_1$ is rotated $\theta$ and then uniformly scaled by a factor $k$ to exactly fit within $r_2$. I'm trying to find the value of $\theta$ that maximizes $k$, ...
2
votes
1answer
33 views

Analyse trigonometrical function

Function is $f(x)=\sin^3x+\cos^3x$ I'm confused when I need to solve $f(x)=0$ cause I got different values for the same x. Also need help with $\lim_{x \to \pm \infty} \sin^3x+\cos^3x$ Thanks
1
vote
1answer
280 views

Rotation vs lift distance

I'm working on a homework problem and I think I found an answer, but not positive. Here is the question: A winch with a $6$-inch radius is used to lift a container. The winch is designed so that as ...
1
vote
3answers
167 views

Prove that if $\theta$ is an angle with $\cos(2\theta)$ irrational then $\cos \theta$ is also irrational

Prove that if $\theta$ is an angle with $\cos(2\theta)$ irrational then $\cos \theta$ is also irrational. (hint: recall that $\cos(2\theta)=2\cos^2(\theta)-1$ )
2
votes
4answers
686 views

Proof of $\arctan{2} = \pi/2 -\arctan{1/2}$

I am studying undergraduate complex analysis, and in my Textbook the author claimed that $$\arctan(2)=\frac{\pi}{2}-\arctan\left(\frac{1}{2}\right)$$ when he was doing an example regarding to ...
1
vote
3answers
892 views

Velocity vectors and trigonometry

I am trying to learn about velocity vectors but this word problem is confusing me. A boat is going 20 mph north east, the velocity u of the boat is the durection of the boats motion, and length is ...
2
votes
2answers
72 views

Infinite arctan series

I know that usually these types of problems deal with pattern recognition. There would be specific pattern as one proceeds from one term to another. But, in this problem I'm unable to recognize one. ...
1
vote
3answers
431 views

Curve to fit points

I'm trying to find the equation that fits the following points: $1,0.0105; 2,0.181; 3,0.47; 4,0.755; 5,1.01; 6,1.22; 7,1.39; 8,1.54; 9,1.67; 10,1.79; 11,1.88; 12,1.96; 13,2.03; 14,2.10; 15,2.15; ...
1
vote
2answers
318 views

Simplifying complex radicals from trigonometric expression

How do I evaluate $ sin(20)$ exactly? [in degrees] I derived the relationship between $sin(x) $ and $sin(3x)$ where $x = sin(x)$ and $ y = sin(3x)$ ...
0
votes
1answer
82 views

What is the sine of arcsine of $x$? Problem with using trigonometric substitution in integral.

I'm having problems with this $\int \sqrt{1-x^2}\,dx$. Now the text book (Spivak's Calculus) says we can replace $x$ by $\sin u$ ($u = \arcsin x$). Now my question is how can we replace $u$ by ...
2
votes
1answer
380 views

Tide and Trigonometric functions

I have a tide guide that gives me four readings for the day - 2 high tides and two low tides. This means it completes two full revolutions within a day. What I'm having trouble with is taking the four ...
0
votes
1answer
53 views

Trigonometric functions properties

So I have a test next week and I have this question which I do know how to solve and I have no direction how to prove that. Any help would be appreciated. $$ \forall (x_{1}\land x_{2}) \in ...
4
votes
1answer
113 views

Calculate the X,Y values of an ellipse

I guess am confused somewhere. I have the length(l) and breadth(b) of an ellipse enclosing rectangle. I know the center point and the angle(x) that the line makes with the center. I want to know the ...
3
votes
1answer
49 views

trigonometry and integral properties

So' I have a test next week and I need to answer some question as fast as I can (true or false question). So I have the following question: $$\int\limits_u^1 \frac{1}{1+x^{2}} = ...