The unit circle, the trigonometric functions and their reciprocals | Trigonometry | Python Turtle
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Timestamps available below
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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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You can get the Python script that generates the animation from my Patreon page, namely https://patreon.com/Sohcahtoa1609.
Playlists
1) Geometry: https://youtube.com/playlist?list=PLRhAOTDGDH-vwWnktVuvAaPD44blf90KL
2) Trigonometry: https://youtube.com/playlist?list=PLRhAOTDGDH-sec0WnQUZoHBuwY0-q7WNn
3) Conic sections: https://youtube.com/playlist?list=PLRhAOTDGDH-t9Hwr0Lr3cDVevHqhWQeXb
4) Circles: https://youtube.com/playlist?list=PLRhAOTDGDH-vhHMUU5fcffH8nLtfxbmcq
5) Ellipses: https://youtube.com/playlist?list=PLRhAOTDGDH-uO16UdmlBZ4T6nLycEBn-J
6) Parabolas: https://youtube.com/playlist?list=PLRhAOTDGDH-vEIjaIHvVqyvMq3BM8Yqk6
7) Hyperbolas: https://youtube.com/playlist?list=PLRhAOTDGDH-u4LMV8KTwephMTjEg1wZnE
8) Pencils: https://youtube.com/playlist?list=PLRhAOTDGDH-uMtFWmHz8yeBrXwSfOKy7g
9) Triangles: https://youtube.com/playlist?list=PLRhAOTDGDH-snS_7gm92FUMzrDJSCqT1W
10) Quadrilaterals: https://youtube.com/playlist?list=PLRhAOTDGDH-uNewJxnedw2shXIC8kgVUd
You can support my work on
i) Patreon: https://patreon.com/Sohcahtoa1609
ii) Facebook: https://facebook.com/Sohcahtoa1609
iii) Twitter: https://twitter.com/Sohcahtoa1609
iv) Instagram: https://instagram.com/sohcahtoa1609
Don’t forget to click on the red SUBSCRIBE button. Then, click on the bell and select the option “All” from the drop-down list, to be the first to know when a new video is released.
Lastly, a disclaimer: this video is meant to be a proof of concept.
#Sohcahtoa1609
Видео The unit circle, the trigonometric functions and their reciprocals | Trigonometry | Python Turtle канала Sohcahtoa1609
Support my work on Patreon: https://patreon.com/Sohcahtoa1609
Timestamps available below
/* *** *** *** *** *** *** *** */
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.
/* *** *** *** *** *** *** *** */
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
/* *** *** *** *** *** *** *** */
You can get the Python script that generates the animation from my Patreon page, namely https://patreon.com/Sohcahtoa1609.
Playlists
1) Geometry: https://youtube.com/playlist?list=PLRhAOTDGDH-vwWnktVuvAaPD44blf90KL
2) Trigonometry: https://youtube.com/playlist?list=PLRhAOTDGDH-sec0WnQUZoHBuwY0-q7WNn
3) Conic sections: https://youtube.com/playlist?list=PLRhAOTDGDH-t9Hwr0Lr3cDVevHqhWQeXb
4) Circles: https://youtube.com/playlist?list=PLRhAOTDGDH-vhHMUU5fcffH8nLtfxbmcq
5) Ellipses: https://youtube.com/playlist?list=PLRhAOTDGDH-uO16UdmlBZ4T6nLycEBn-J
6) Parabolas: https://youtube.com/playlist?list=PLRhAOTDGDH-vEIjaIHvVqyvMq3BM8Yqk6
7) Hyperbolas: https://youtube.com/playlist?list=PLRhAOTDGDH-u4LMV8KTwephMTjEg1wZnE
8) Pencils: https://youtube.com/playlist?list=PLRhAOTDGDH-uMtFWmHz8yeBrXwSfOKy7g
9) Triangles: https://youtube.com/playlist?list=PLRhAOTDGDH-snS_7gm92FUMzrDJSCqT1W
10) Quadrilaterals: https://youtube.com/playlist?list=PLRhAOTDGDH-uNewJxnedw2shXIC8kgVUd
You can support my work on
i) Patreon: https://patreon.com/Sohcahtoa1609
ii) Facebook: https://facebook.com/Sohcahtoa1609
iii) Twitter: https://twitter.com/Sohcahtoa1609
iv) Instagram: https://instagram.com/sohcahtoa1609
Don’t forget to click on the red SUBSCRIBE button. Then, click on the bell and select the option “All” from the drop-down list, to be the first to know when a new video is released.
Lastly, a disclaimer: this video is meant to be a proof of concept.
#Sohcahtoa1609
Видео The unit circle, the trigonometric functions and their reciprocals | Trigonometry | Python Turtle канала Sohcahtoa1609
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