The unit circle, the trigonometric functions and their reciprocals | Trigonometry | Python Turtle

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There are three basic trigonometric functions, namely sine (sin), cosine (cos) and tangent (tan). Each of these three trigonometric functions has a reciprocal: cosecant (csc) is the reciprocal of sine; secant (sec) is the reciprocal of cosine; and cotangent (cot) is the reciprocal of tangent. These six trigonometric functions can be thought of as segments. The cosine function is the x-coordinate (abscissa), and the sine function is the y-coordinate (ordinate) of any point on the unit circle. Based on the cosine and sine functions and the three Pythagorean identities, we can derive the other four segments. Because they change their length with the central angle θ, these segments help us to better understand the graphs of the trigonometric functions.

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00:00 Patreon ad
00:09 Intro
00:26 The trigonometric functions as line segments
01:07 Graphing the three basic trigonometric functions, namely the sine, the cosine and the tangent
02:05 Graphing the sine and its reciprocal, namely the cosecant
02:50 Graphing the cosine and its reciprocal, namely the secant
03:34 Graphing the tangent and its reciprocal, namely the cotangent
04:31 Graphing all three reciprocals, namely the cosecant, the secant and the cotangent
05:39 Support my work on social media

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Playlists
1) Geometry:    • Geometry  
2) Trigonometry:    • Trigonometry  
3) Conic sections:    • Conic sections (geometry)  
4) Circles:    • Circles (geometry)  
5) Ellipses:    • Ellipses (geometry)  
6) Parabolas:    • Parabolas (geometry)  
7) Hyperbolas:    • Hyperbolas (geometry)  
8) Pencils:    • Pencils (geometry)  
9) Triangles:    • Triangles (geometry)  
10) Quadrilaterals:    • Quadrilaterals (geometry)  

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