Computing sine and cosine is non-trivial for general angles — we need Taylor series (or similar tools) to do this. However there are some special angles (usually small integer fractions of $\pi$) for which we can use a little geometry to help. Consider the following two triangles.
The first results from cutting a square along its diagonal, while the second is obtained by cutting an equilateral triangle from one corner to the middle of the opposite side. These, together with the angles $0,\frac{\pi}{2}$ and $\pi$ give the following table of values
 $\theta$ $\sin\theta$ $\cos\theta$ $\tan\theta$ $\csc\theta$ $\sec\theta$ $\cot\theta$ $0$ rad 0 1 0 DNE 1 DNE $\tfrac{\pi}{2}$ rad 1 0 DNE 1 DNE 0 $\pi$ rad 0 -1 0 DNE -1 DNE $\tfrac{\pi}{4}$ rad $\tfrac{1}{\sqrt{2}}$ $\tfrac{1}{\sqrt{2}}$ 1 $\sqrt{2}$ $\sqrt{2}$ 1 $\tfrac{\pi}{6}$ rad $\tfrac{1}{2}$ $\tfrac{\sqrt{3}}{2}$ $\tfrac{1}{\sqrt{3}}$ 2 $\tfrac{2}{\sqrt{3}}$ $\sqrt{3}$ $\tfrac{\pi}{3}$ rad $\tfrac{\sqrt{3}}{2}$ $\tfrac{1}{2}$ $\sqrt{3}$ $\tfrac{2}{\sqrt{3}}$ 2 $\tfrac{1}{\sqrt{3}}$