Finding the value of trigonometric function of any angle? Whenever I have to calculate the value of a given trigonometric function for an angle, I always refer to a table similar to this: 

But what if I want to find the value for sin$\theta$, where $\theta$ = 32$^{\circ}$ or $\theta$ = 49$^{\circ}$ or for any function, for that matter.
 A: *

*I think it could be a good idea you switch from degrees to radians.

*You can find more detailed tables than the one you put in your post

*Now, suppose than you need  the value of $\sin(\frac{32 \pi}{180})$ (which is your $32$ degrees). One of the ways is to use series centered at a point where you know the values. For this specific case, let use write $$\sin(\frac{32 \pi}{180})=\sin(\frac{30 \pi}{180}+\frac{2 \pi}{180})=\sin(\frac{ \pi}{6}+\frac{\pi}{90})$$ Now, we shall consider the development of $\sin(a+x)$ built at $x=0$ $$\sin(a+x)=\sin (a)+x \cos (a)-\frac{1}{2} x^2 \sin (a)-\frac{1}{6} x^3 \cos (a)+\frac{1}{24}
   x^4 \sin (a)+O\left(x^5\right)$$ in which you know the values of $\sin(a)$ and $\cos(a)$. For $a=\frac{\pi}{6}$, this just write $$\sin(\frac{ \pi}{6}+x)=\frac{1}{2}+\frac{\sqrt{3} x}{2}-\frac{x^2}{4}-\frac{x^3}{4
   \sqrt{3}}+\frac{x^4}{48}+O\left(x^5\right)$$ Now, replace $x=\frac{ \pi}{90}$ and compute; you would obtain a value of $0.529919263860$ while the exact number is $0.529919264233$. For sure, if you need less accuracy, use less terms.
