Explanation of SOH CAH TOA I understand that SOH CAH TOA represents a ratio. However, is there any proof or explanation that someone without knowledge on series can understand on how sin cos tan came about? I read my textbook and look on Wikipedia but my knowledge is still practically where I started. Could someone please explain to me the theorem that can be explained to someone whose knowledge is limited to calculus.

Recall that trigonometric functions are defined geometrically and notably

* $\cos x$ and $\sin x$ are the coordinates of the point $M$ on the trigonometric circle
* $\tan x$ is the $y$ coordinate of the intersection between the vertical line from $(1,0)$ and the line $OM$



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from here we derive immediately the foundamental relationships $\sin^2 \theta + \cos^2 \theta =1$ and the one you are looking for

$$\tan \theta=\frac{\sin \theta}{\cos \theta}$$