# trigonometry

Published articles for trigonometry.

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## Learning to Love Complex Numbers

DevFeed: [Learning to Love Complex Numbers](<https://devfeed.tech/articles/learning-to-love-complex-numbers-40358.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/05/26/learning-to-love-complex-numbers/>)

Published: 2014-05-26T09:00:48Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Learning](<https://devfeed.tech/topics/learning.md>)

Tags: [complex](<https://devfeed.tech/tags/complex.md>), [complex-numbers](<https://devfeed.tech/tags/complex-numbers.md>), [fractals](<https://devfeed.tech/tags/fractals.md>), [graphics](<https://devfeed.tech/tags/graphics.md>), [learning](<https://devfeed.tech/tags/learning.md>), [mandelbrot-set](<https://devfeed.tech/tags/mandelbrot-set.md>), [python](<https://devfeed.tech/tags/python.md>), [trigonometry](<https://devfeed.tech/tags/trigonometry.md>)

### AI overview

An introductory post for readers with some programming experience and no prior mathematical background. It explains numbers as human-invented mathematical concepts and begins approaching complex numbers through the development of zero, negative numbers, fractions, square roots, and patterns in perfect squares.

### Source excerpt

This post is intended for people with a little bit of programming experience and no prior mathematical background. So let's talk about numbers. Numbers are curious things. On one hand, they represent one of the most natural things known to humans, which is quantity. It's so natural to humans that even newborn babies are in tune with the difference between quantities of objects between 1 and 3, in that they notice when quantity changes much more vividly than other features like color or shape.

## Double Angle Trigonometric Formulas

DevFeed: [Double Angle Trigonometric Formulas](<https://devfeed.tech/articles/double-angle-trigonometric-formulas-40273.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/05/19/double-angle-trigonometric-formulas/>)

Published: 2012-05-19T23:28:53Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>)

Tags: [cos](<https://devfeed.tech/tags/cos.md>), [double-angle-identities](<https://devfeed.tech/tags/double-angle-identities.md>), [geometric-transformations](<https://devfeed.tech/tags/geometric-transformations.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrices](<https://devfeed.tech/tags/matrices.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [rotation](<https://devfeed.tech/tags/rotation.md>), [trigonometry](<https://devfeed.tech/tags/trigonometry.md>), [vector](<https://devfeed.tech/tags/vector.md>)

### AI overview

This tutorial derives the double-angle sine and cosine identities by representing planar rotations with a 2x2 matrix, squaring that matrix, and comparing it with a rotation by 2θ.

### Source excerpt

Problem: Derive the double angle identities $$\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\ \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$$ Solution: Recall from linear algebra how one rotates a point in the plane. The matrix of rotation (derived by seeing where $ (1,0)$ and $ (0,1)$ go under a rotation by $ \theta$, and writing those coordinates in the columns) is $$A = \begin{pmatrix} \cos(\theta) & -\sin(\theta) \\\ \sin(\theta) & \cos(\theta) \end{pmatrix}$$ Next, note that to rotate a point twice by $ \theta$, we simply multiply the point (as a vector) by $ A$ twice.