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11,262 Views • Oct 17, 2024 • Click to toggle off description
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In this video, we break down what sine, cosine, and tangent really mean by looking at their relationship to the unit circle. Honestly, "trigonometry" should probably be called "circle-ometry." If you want to understand how these functions tie directly to the geometry of circles, this is the place to start.
Cosine gives you the x-coordinate of a point on the unit circle, while sine gives you the y-coordinate. Tangent? It's either the ratio of sine to cosine (y/x) or, even better, the slope of the line at that angle. Everything comes back to the geometry of circles.
#trigonometry #unitcircle #mathexplained
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Views : 11,262
Genre: Education
License: Standard YouTube License
Uploaded At Oct 17, 2024 ^^
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RYD date created : 2024-10-29T21:20:13.75258Z
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23 Comments
Top Comments of this video!! :3
This is such a fun way to display their definitions, I memorized Horizontal and Vertical components for Mechanics but this makes it very intuitive Thank you
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Hey man! Just got a TI-Nspire CX ii and wanted to thank you for making the tutorial on plotting tables 2 years ago. Still holds up like it was made today!
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My way was always building off of my memorized definition of slope. Rise over run = slope was replaced with sine over cosine = tangent. If I needed to fine the sine, that was the rise, or the y coordinate on a circle. If I wanted to get the cosine that was the run, or the x coordinate on a circle. Makes it super intuitive, and helps build on previous knowledge.
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You're a cool teacher
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I'd have said sine cosine to be a derivative of Pythogorus theorem which immediately implies sin^2 x + cos ^2 x = 1. From my perspective , unit circle way seems to be more complicated to understand for the first timers.
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This didnt click for me until calc 2😒
I was always told to just memorize it and i cant remember shit.
Understanding>memorizin
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And the angle in radians is the length of the arc
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It's not hard to come up with an intuitive way. They are the ratios of sides of a right triangle. For example if you fix the length of the hypotenuse and vary it's angle, the sides trade off proportionally
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Im sorry I’ll be needing a moment
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But isn’t sin and cosine the ratio between sides on a triangle well at least isn’t that the original definition
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Hi Mr. R it’s Allergies 🎊
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How about tan?
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@isaaccollazo2828
2 months ago
This was exactly how my Precalc teacher in high school taught it, and I can recite the unit circle from memory because of it.
Props to you for showing off trig’s beautiful simplicity, teachers don’t do it enough.
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