I want some intuitive understanding of the trigonometric functions. One way is to understand ways they can be computed when just an angle in degrees or radians is given. The sine of an angle is defined as the ratio of two sides of a right triangle. If this is the case then I can't find a way to compute it without requiring sine.
To compute the sine of an angle:
1) Create right triangles.
2) Compute their angles.
3) Once a right triangle with the correct angle (or close enough) is found. Compute the opposite/hypotenuse ratio.
The problem: Step 2 requires computing angles of right triangles. The way to do this appears to be to compute the opposite/hypotenuse ratio and use the inverse of sine to find the angle. The inverse of sine seems to require similar steps only this time find a triangle with the correct ratio, instead of correct angle, and then compute the angle of that triangle which seems to be to use...the inverse of sine.
How do I compute the sine of an angle without requiring a sine function within the sine function I'm trying to create?