Explanation:
imagine the red dot (the triangle vertex with the marked angle theta) is the center of the circle, and the circle passes through the blue dot.
rotate the triangle up a little bit around the red dot, so that 48 is horizontal, and 55 vertical.
then this triangle is a trigonometric triangle.
so, 73 is the radius (going from the center of the circle to the circle arc).
we know sine is the up/down distance of the point on the circle arc from the circle center.
and cosine is the left/right distance of the point on the circle arc from from the circle center.
and then, don't forget : the trigonometric functions represent these distances in a norm circle (radius = 1).
all the corresponding distances in a larger circle and triangle are the basic trigonometric functions multiplied by the actual radius (scaling factor).
so,
55 = sin(theta) × 73
sin(theta) = 55/73 = 0.753424658...
48 = cos(theta) × 73
cos(theta) = 48/73 = 0.657534247...
tangent = sine/cosine
tan(theta) = 55/73 / 48/73 = (55×73)/(73×48) =
= 55/48 = 1.145833333...
cosecant = 1/sine
csc(theta) = 1 / 55/73 = 73/55 = 1.327272727...
secant = 1/cosine
sec(theta) = 1 / 48/73 = 73/48 = 1.520833333...
cotangent = 1/tangent
cot(theta) = 1 / 55/48 = 48/55 = 0.872727273...
as you can see : the trigonometric functions are really that easy.
FYI : using the inverse of these functions we see that
theta = 48.88790956...°