Approximating Cosine

If you know how to do the sine approximation for angles between 0 and 90, then you already know how to do the same for cosine because cos(x) = sin(90-x) meaning that if you want the cosine of 20 degrees it's equal to the sine of 70 degrees which you already know how to do from the above.

Approximating Tangent

We know that tan(x) = sin(x)/cos(x) and we know that cos(x) = sin(90-x) so we know that tan(x) = sin(x)/sin(90-x), which we know how to find from the sine approximation, though it's going to be a lot easier to keep things straight if you right down each of the results for sin(x) and sin(90-x) as you go.

Approximating Secant, Cosecant, Cotangent

We know that csc(x) = 1/sin(x), sec(x) = 1/cos(x), and cot(x) = 1/tan(x) so when we get that fraction at the end of our algorithm we can just "flip it" to get the other trig function values.

I'll see what else I can dig up.