Question 564699
You didn't provide any diagrams. I think you are referring to a triangle that looks something like this:


{{{drawing(200,200,0,10,0,10,


triangle(2,2,8,2,8,7),
locate(2,2,O),
locate(5,2,b),
locate(8.4,4.5,a),
locate(5,5.4,1),
locate(3,3,theta)
)
}}}


Suppose that this triangle is part of the unit circle with radius 1 and origin O(0,0). Then


*[tex \LARGE \sin(\theta) = \frac{opp}{hyp} = \frac{a}{1} = a]
*[tex \LARGE \cos(\theta) = \frac{adj}{hyp} = \frac{b}{1} = b]


Other trig functions (tan, csc, etc.) should follow. Note that b and a are simply the x- and y-coordinates of a point on the unit circle.