Question 386499
You can do sine, cosine, tangent measurements of an angle less than 90 degrees using right triangles using the three definitions:

{{{sin x = a/c}}}


{{{cos x = b/c}}}


{{{tan x = a/b}}}


where a is the segment opposite the angle x, b is the segment "adjacent" to x but not the hypotenuse, and c is the hypotenuse (always note that the hypotenuse is the side opposite the right angle).


The most general way to do sine, cosine, tangent is to consider a circle graphed in the xy-plane that has radius 1 (called the unit circle). For some point on the circle, we can determine the angle from the x-axis given that counterclockwise motion denotes a positive angle. The sine of the angle is the y-coordinate of the point, and the cosine of the angle is the x-coordinate. It is easy to see afterward that the Pythagorean identity is verified:


{{{sin^2 (x) + cos^2 (x) = 1}}}