Questions tagged [trigonometry]
For challenges where trigonometry plays an important role.
36 questions
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Inverse trigonometric functions
There are 3 (commonly used) trigonometric functions sin cos and tan each of these functions ...
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Cutting a Circular Pizza Vertically
Most people would cut circular pizzas into circular sectors to divide them up evenly, but it's also possible to divide them evenly by cutting them vertically like so, where each piece has the same ...
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Ptolemy's table of chords
Ptolemy's Almagest contains a table of chords that effectively served as the world's only comprehensive trigonometric table for over a millennium. In modern form it looks like this:
\begin{array}{|l|...
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Compute the Three Dimensional Discrete Cosine Transform
Challenge
I've checked that there is a question Compute the Discrete Cosine Transform which is a competition for implementing a shortest solution to compute the one dimensional discrete cosine ...
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Integers in cosine
Integers in cosine
From trigonometry we know that
\$\sin(a) =-\cos(a + \frac{(4*m + 1)\pi}{2})\$
where \$a\$ is an angle and \$m\in\mathbb{Z}\$ (integer).
The task
For an input of a positive integer \$...
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Perimeter of Conway hexagon
Background
Given a triangle \$ABC\$, extend its three sides by the opposite side length, as shown in the figure below. Then the six points surprisingly lie on a circle called the Conway circle, whose ...
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Are my triangles similar?
Given (in any structure; flat list, two lists of lists, a tuple of matrices, a 3D array, complex numbers,…) the coordinates for two non-degenerate triangles ...
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Black Box Trigonometry
Write a program or function that can distinguish the following 12 trigonometric functions: sin,
cos,
...
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Distance between two points on the Moon
Given latitude/longitude of two points on the Moon (lat1, lon1) and (lat2, lon2), compute the distance between the two points in ...
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Expand Sine and Cosine
Trigonometry has LOTS of identities. So many that you can expand most functions into sines and cosines of a few values. The task here is to do that in the fewest bytes possible.
Identity list
Well, ...
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answers
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Approximate the Dottie number to arbitrary precision
The Dottie number is the fixed point of the cosine function, or the solution to the equation cos(x)=x.1
Your task will be to make code that approximates this constant. Your code should represent a ...
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Solve sin(θ) = x in the range a ≤ θ ≤ b
Challenge
Given a number, x where -1 ≤ x ≤ 1, and the integers a and ...
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Compute the Discrete Cosine Transform
Implement the Discrete Cosine Transform (DCT). This may implemented as either a function or a program and the sequence can be given as either an argument or using standard input. Your program must be ...
user69099
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answers
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Find the coterminal angle on [0, 2π)
This challenge is very simple:
Given an angle measure in degrees or radians (your choice), output the angle between 0 and 2π non-inclusive [0º, 360º) that is coterminal with it.
Input
A positive ...
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The Pedant's Cosine
My boss just told me to write a cosine function. Being a good math geek, my mind immediately conjured the appropriate Taylor Series.
$$\cos(x) = \frac 1 {0!} - \frac {x^2} {2!} + \frac {x^4} {4!} - \...
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Draw a graph of \$y=(-n)^x\$
Challenge
Given an input of an integer, \$n\$ (where \$0<n<50\$), output the graph of \$y=\mathrm{Re}((-n)^x)\$ from \$x = -3\$ to \$x = 3\$ inclusive.
Where \$\mathrm{Re}(p)\$ is the real part ...
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Help me I'm lost in the ocean!
Introduction
Today I went fishing alone with my canoe, unfortunately I fell asleep and the stream brought me away, I lost my oars, now it's night and I am lost in the ocean! I can't see the coast so ...
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Distance Between Two Points Travelling on a Polar Graph Chart
Brief Problem Explanation
Write a program to find the minimum distance between two points traveling only on rays emanating from the origin and circles centered on the origin.
Explanation of Premise
...
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Write a Sine-Deriving Machine
The Challenge
Your challenge is to write a program that evaluates the following function:
f(x, t) = d^x / dt^x (sin t)
That is, the x-th derivative of sin t. In case you aren't familiar with ...
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15
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golf atan2
Sometimes it really is a struggle to convert Cartesian coordinates (x,y) to Polar coordinates (r,phi). While you can calculate <...
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Matrix Trigonometry
Introduction
The two most common trigonometric functions, sine and cosine (or sin and ...
user45941
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Print cos(2π/17) exactly
One way to construct a regular heptadecagon starts with drawing a horizontal line of length 1 from the center to a vertex. Then the distance along that line from ...
- 13.9k
9
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answer
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Print sin, cos, and tan of special angles
In trigonometry, there are certain angles known as "special angles". This is because when you take sin, cos or tan of one of these angles, you get a result that is easy to remember because it is a ...
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Make a Surfin' Word
Your goal is to map a piece of text to a sine curve of the form:
a sin ( mx - b )
Where a and m are non-zero rational numbers, b is a rational number, and the calculations are in radians.
It doesn't ...
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Finding Exclusive Area in Circle Intersections
Here's a deceptively challenging geometry puzzle for you!
Given a circle A, and n other circles ...
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2
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Spherical excess of a triangle
Spherical excess of a triangle
As we all know, the sum of angles of any planar triangle is equal to 180 degrees.
However, for a spherical triangle, the sum of angles is always greater than 180 degrees....
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47
answers
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A single pixel moving in a circular path
This is a graphical output challenge where the task is to give the shortest code per language.
Task
Your code should plot a single purple pixel (hex value #800080 or
rgb(128, 0, 128)), moving ...
user9206
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votes
18
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Find the angle between two points
Given two points A and B, find the angle from line AO to line ...
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Regular Polygrams
Given the number of vertices n ≥ 3 and the "step size" 1 ≤ m < n/2 (indicating the distance between two connected vertices), ...
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A Sine of Greatness
Introduction
Everyone's heard of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). Nearly every angle has them.
Far less known, or remembered, are the ...
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Help me with trigonometry!
Thank you guys so much for your help with calculus. Now I need some help with my upcoming trigonometry test.
On the test, I'll need to simplify expressions. I’ll be given input like ...
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Output an Animated Trigonometry Circle
I want you to write a program that outputs a trigonometry circle like the one below. I also want you to animate this circle, having the sine line move along the circumference with the other lines move ...
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Fast Trig Calculation
Fast Trigonometry Calculations
Your task is to create a program which can calculate the sine, cosine and tangent of an angle in degrees.
Rules
No built-in trigonometry functions (not even secant, ...
user16402
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18
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Let the trigonometry begin!
Introduction:
The sine of \$x\$ is given by the formula:
$$\sin(x) = x - \frac {x^3}{3!} + \frac {x^5}{5!} - \frac {x^7}{7!} + \frac {x^9}{9!} - \frac {x^{11}}{11!} + \cdots$$
The cosine of \$x\$ is ...
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Draw a regular polygon
The goal of this code golf is to draw a regular polygon (one with equal side lengths) given the number of sides and radius (distance from center to vertex).
The number of sides and the radius can be ...
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Solving triangles with trigonometry
Time to dig up your old trigonometry notes from high school! The challenge is to solve the unknown sides and angles of different triangles. And as is customary in code golf, the smallest working code ...
user1158