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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 $(x, y) = x^2+y^2=1, y=x$.

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  • $\begingroup$ Impossible..... $\endgroup$ – William Elliot Feb 29 at 20:43
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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.

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