Trigonometric functions for specific angles

Values of trigonometric functions at specific angles:

For 0° and 90°: These functions are limiting values that can be observed from the drawing. As side $y$ approaches 0 (zero), the $x$ approaches $r$ .

\sin (0 °) = lim_{y \to 0} (\frac{y}{r}) = \frac{0}{r} = 0 = \cos (90 °)

\cos (0 °) = lim_{x \to r} (\frac{x}{r}) = \frac{r}{r} = 1 = \sin (90 °)

\tan (0 °) = lim_{y \to 0} (\frac{y}{x}) = \frac{0}{x} = 0 = \cot (90 °)

\begin{array}{l} \sin (30 °) = \frac{a}{2 a} = \frac{1}{2} = 0.5 = \cos (60 °) \\ \cos (30 °) = \frac{a \sqrt{3}}{2 a} = \frac{\sqrt{3}}{2} = 0.866 = \sin (60 °) \\ \tan (30 °) = \frac{a}{a \sqrt{3}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} = 0.577 = \cot (60 °) \\ \cot (30 °) = \frac{a \sqrt{3}}{a} = \sqrt{3} = 1.732 = \tan (60 °) \end{array}

\begin{array}{l} \sin (45 °) = \frac{a}{a \sqrt{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} = 0.707 = \cos (45 °) \\ \tan (45 °) = \frac{a}{a} = 1 = \cot (45 °) \end{array}