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I have a challenge in explaining the concepts of sine, cos and tan of trigonometry to a kid, as he just doesn’t seem to get it right. Is there a better method of explaining these concepts by relating it to some physical nature of the world so that the kid gets the concept right?

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    $\begingroup$ Do you remember how you learned it? I typically start off my intro to trig lessons with similar triangles. $\endgroup$ Sep 4, 2019 at 22:13
  • $\begingroup$ I would follow the same approach by starting off with triangles but the kid just gets confused on which side of triangle to pick and mixes up things. The reason for the post is to find out if there is some memorisable technique which the kid could employ to avoid the confusion! $\endgroup$ Sep 4, 2019 at 22:25
  • $\begingroup$ Just so I understand. Does he have a problem pointing out the side that is opposite of an angle. Opposite means the side away from the angle. In other words it doesn't help to create the angle being spoke about. $\endgroup$
    – randomgirl
    Sep 4, 2019 at 22:50
  • $\begingroup$ My document "(Almost) Everything You Need to Remember about Trigonometry, in One Simple Diagram" (PDF) gives something of a conceptual overview of trig fundamentals based on what I fittingly call the Fundamental Trigonograph. In its current, still-somewhat-drafty, form, the note serves more of a refresher than an introduction, but my ultimate goal is to push it more towards the latter. $\endgroup$
    – Blue
    Sep 5, 2019 at 0:46
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    $\begingroup$ @Blue This is just fantastic! Thanks for the document. It really helps!! $\endgroup$ Sep 5, 2019 at 3:17

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One (The most?) important thing to start is to understand the concept of "similar triangles".

Consider the picture of a right triangle with hypotenuse equal to $1$. Of course, the two catetis are equal to $\sin(\theta)$ and $\cos(\theta)$.

Suppose that the kid is looking this on a smartphone. If he/she zooms with two fingers the screen of the smarthphone, then what he/she gets is a longer/shorter hypotenuse. The two catetis increased/decreased their length of the same factor of the hypotenuse.

This concept is sometimes (or many times?) tricky for older "kids" in college :D

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