is there a way to solve sine, cosine, and tangent without the use of a calculator?
Yes. There is an infinite series in each case to calculate the function that you want, but will take you at least an hour to get 5-10 accurate decimal places.
Example: find the Sin(.25) in radians: You can use Taylor's infinite series for sine, which goes like this: sin(.25)=.25 - .25^3/3! + .25^5/5! - .25^7/7! + .25^9/9!..........and so on. Each term will give you 1-2 accurate decimal places.
Sine:
You could leave it in an unsimplified form as such:
There are three sides of a triangle: a = 12, b, c
The angles are as such: A = 30o, B = 40o, C
\(a/\sin(A) = b/\sin(B) \Rightarrow 12/\sin(30°) = b/\sin(40°) \Rightarrow 12*\sin(40°) = b*\sin(30°) \Rightarrow b = (12*\sin(40°))/\sin(30°)\)
