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 April 13th, 2018, 03:26 AM #1 Member   Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0 Sines and Cosines Can somebody please explain sines and cosines to me and how they work? Thank you very much in advance. Last edited by greg1313; April 13th, 2018 at 03:56 AM.
 April 13th, 2018, 03:57 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,900 Thanks: 1093 Math Focus: Elementary mathematics and beyond Do you have any specific questions about them?
 April 13th, 2018, 04:15 AM #3 Member   Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0 Just what they are and how you use them.
 April 13th, 2018, 04:35 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 Math Focus: Mainly analysis and algebra That's too big a subject to teach on here. You should do some reading and come here with questions on any specific points that confuse you. You might start here: https://en.wikipedia.org/wiki/Trigonometry Thanks from topsquark
 April 13th, 2018, 02:10 PM #5 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 If you have a right triangle with angle 90 degrees, t degrees, and 90- t degrees (So that totals 90+ t+ 90-t= 180 degrees. In radians, that would be $\displaystyle \pi/2+ t+ \pi/20- t= \pi$ radian). There will be one side that does not have angle t at either end. That is the "opposite side". There is one side that has the angle t at one end, the right angle at the other. Call that the "near side". The "hypotenuse" is the side opposite the right angle. Call the length of the hypotenuse c, the "near side", b, and the "opposite side", c. The "cosine of t", written as "cos(t)" is defined as "near side divided by hypotenuse" and "sine of t", written as "sin(t)" is the "opposite side divided by hypotenuse". It would help if you would tells us what grade you are in school and what you do know about trigometry.
 April 13th, 2018, 10:56 PM #6 Member   Joined: Oct 2017 From: Japan Posts: 62 Thanks: 3 Students usually find it easier to understand sine and cosine within the framework of the unit circle. I made a few lessons on the topic, check them out and let me know if you have any question.
April 13th, 2018, 11:46 PM   #7
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Quote:
 Originally Posted by rudimt Students usually find it easier to understand sine and cosine within the framework of the unit circle.
I do wholeheartedly agree with you that it's all about the unit circle. I'm of the belief that SOHCAHTOA should be banished from the curriculum. Nobody understands it and then they have to memorize other arcane incantations for the other three quadrants.

With cos and sin defined as the x- and y-coordinates of points on the unit circle, you immediately connect angle measure, which people understand from geometry, with radian measure, the distance along the unit circle. They learn a more sophisticated way of viewing angle measure. And there's no problem of quadrants because you're just reading off the coordinates.

So I very much dislike the fact that even today, when teachers should know better, we still torment the kids with the opposite and adjacent business. That point of view was appropriate when we used sines and cosines to figure out how big our wheat field was. But today, we use sines and cosines to make Fourier series to do digital signal processing that enables the entire world to communicate over wires and through the air. Today it's the functional aspect of sines and cosines that we care about; and we don't care at all about solving triangles to measure wheat fields. Even the wheat farmers just punch the numbers into the computer. Nobody needs to solve triangles any more. Everyone needs to understand that the modern digital world runs on sines and cosines. And the key to it all is the humble unit circle.

Sadly, the educators have not gotten the message.

Last edited by Maschke; April 13th, 2018 at 11:51 PM.

 April 16th, 2018, 12:28 AM #8 Senior Member   Joined: Apr 2014 From: UK Posts: 895 Thanks: 328 I understand SohCahToa But I do find myself agreeing, to the point where perhaps we should teach Rads first (degs only being needed for backwards compatibility, like pints and gallons). I'm not sure how much of the problem is the educators or the bureaucrats who decide on the curriculum...

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