Sine, cosine and tangent in the trigonometric circumference

sine of an angle
Consider a point R on the circumference and its projection on the vertical axis, point R’. We will call the vertical axis the sine axis. The OR’ segment will be the sine of PR.
Note: Check the existence of the right triangle ORR’.

Cosine of an angle
Consider a point R on the circumference and its projection on the horizontal axis R’. We will call the horizontal axis the cosine axis. The OR’ segment will be the cosine of PR.

tangent of an angle
To obtain the tangent of an arc, we must trace a third axis that tangent point A. By joining the end of arc AX (point X) to center O and extending the radius of the circle, it will intersect the tangent axis.
We then define that if x is in the 1st quadrant, Tgx = AR > 0

by Mark Noah
Graduated in Mathematics
Brazil School Team

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Secant, cosecant and cotangent
Definition and examples.

Fundamental relationship of trigonometry
Relations between sine and cosine.

Trigonometry - Math - Brazil School

Source: Brazil School - https://brasilescola.uol.com.br/matematica/seno-coseno-tangente-circunferencia-trigonometrica.htm

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