Where do Sin, Cos and Tan Actually Come From? - Part 2: Unit Circle Introduction

This video explains the unit circle and how sine and cosine are defined for angles beyond right triangles. What is Pi? -    • What is Pi and Where Does it Actually Come...   6÷2(1+2) = ? -    • 6÷2(1+2) = ? | Correct Answer Inside Final...   Flat Earth Debunked -    • Flat Earth Debunked Mathematically Part 1   A massive thank you to all the members who support this channel - I will keep updating the perks. Subscribe for more free educational videos brought to you by Syed Institute. Like to support our cause and help put out more videos. Comment to give feedback and show your support. Website - http://www.syedinstitute.com Email - [email protected] This video is the second part of the series that explores where sine, cosine, and tangent come from, and the geometric origins of trigonometry. This video focuses on introducing the concept of the unit circle and explains how the unit circle is used to define trigonometric functions. It shows how the definitions of sine and cosine move from being based on right-angled triangles to being based on the unit circle. This allows angles such as sin 90°, sin 120°, and sin 0° to be defined, which do not work using right-angled triangles alone. Sine and cosine values are then defined for angles in all four quadrants, giving a complete range of trigonometric values from 0° to 360°. Using these unit circle values, the graph y = sin(x) is then drawn over the interval 0° to 360°, showing how the sine graph arises from the unit circle. Part 3 will continue by looking at negative trigonometric values as well as trigonometric values greater than 360°. Topics covered: unit circle, sine and cosine, trigonometry explained, trigonometric functions, exact trigonometric values, sine graph, cosine graph, trigonometry for all angles. Chapters 0:00 – Introduction – Recap of Part 1 01:36 – Finding exact trig/trigonometric values for angles 30, 45 and 60 03:23 – Important trigonometry example, solve for y and x 04:40 – Unit Circle Introduction 07:01 – Generate unit circle coordinates in first quadrant for 60, 45 and 30 07:49 – Unit circle definition for sine and cosine 08:38 – Generate trig table for 30, 45 and 60 08:54 – Working out sin 0, cos 0, sin 90 and cos 90 (using unit circle) 09:55 – Extend unit circle values for angles to all four quadrants 12:48 – Completed unit circle diagram with angles and coordinates (and trig table) 13:09 – Graph of the sine function - y = sin(x) between 0 and 360 13:50 – Sine values greater than 360? Negative sine values? Media and business enquiries can be made to [email protected] Thank you for watching and thank you for all your support. Equipment Intel i7 12700k Nvidia RTX 4070 Electro-Voice RE20 Focusrite Scarlett 4i4 4th gen