# Questions tagged [trigonometry]

For challenges where trigonometry plays an important role.

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### By what factor must you divide the perimeter of a circle to return the maximum quantity of sines with terminating decimals? [closed]

This is a question which occurred to me in a dispute about which way of calculating sines leads to the most numerically pleasing results. In particular, with numbers which can be handled exactly. The ...
5k views

### 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. ...
3k views

### 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 ...
649 views

### 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, ...
909 views

### 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 ...
2k views

### 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 ...
1k views

### g​o​l​f​ ​a​t​a​n​2

Sometimes it really is a struggle to convert Cartesian coordinates (x,y) to Polar coordinates (r,phi). While you can calculate <...
5k views

### 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 ...
592 views

### Solve sin(θ) = x in the range a ≤ θ ≤ b

Challenge Given a number, x where -1 ≤ x ≤ 1, and the integers a and ...
4k views

### Black Box Trigonometry

Write a program or function that can distinguish the following 12 trigonometric functions: sin, cos, ...
840 views

### 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 ...
3k views

### 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, ...
8k views

### 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 ...
697 views

### 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 ...
8k views

### 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 ...
434 views

### 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 ...
923 views

### Approximate the Dottie number

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 ...
2k views

### 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 ...
1k views

### 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 ...
2k views

### 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 ...
2k views

### Matrix Trigonometry

Introduction The two most common trigonometric functions, sine and cosine (or sin and ...
900 views

### 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 ...
637 views

### 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 ...
2k views

### 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 ...
4k views

### 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 ...
549 views

### Finding Exclusive Area in Circle Intersections

Here's a deceptively challenging geometry puzzle for you! Given a circle A, and n other circles ...
1k views

### 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 ...
2k views

### Find the angle between two points

Given two points A and B, find the angle from line AO to line ...