# Convert angle of inclination of line to slope without using trig

I would like to solve for the value of sine and cosine by finding the intersection of the unit circle and a line representing the given angle. However, I am not sure how to get the slope of the line with given angle of inclination without using the tangent function, which I can't use because it rids of the idea of calculating the sine and cosine by hand.

For example, sine of $$45^{\circ}$$ would equal $$y$$ in $$(x, y) = x^2+y^2=1, y=x$$.

• Impossible..... – William Elliot Feb 29 '20 at 20:43

No. That's not possible one of the reasons is that $$sin(x)$$ and $$cos(x)$$ can assume all values in $$[-1,1]$$ and not all of them are expressible as functions of $$x$$ (without use of Power Series taught in Calc) or even calculated by hand.