Скачать или смотреть 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.
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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?


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