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# Exact values of trigonometric functions

Table of trigonometric functions (sine, cosine, tangent, cotangent) exact values. The range of degrees is between 0° and 360°.

$$\begin{array}{|c|c|c|c|c|c|} \hline {\text{Deg}} & 0 & 30^{\circ} & 45^{\circ} & 60^{\circ} & 90^{\circ} & 180^{\circ} & 270^{\circ} & 360^{\circ} \\\hline {\text{Rad}} & 0 & {\frac{\pi}{6}} & {\frac{\pi}{4}} & {\frac{\pi}{3}} & {\frac{\pi}{2}} & {\pi} & {\frac{3\pi}{2}} & {2\pi} \\\hline {\sin} & 0 & {\frac{1}{2}} & {\frac{\sqrt{2}}{2}} & {\frac{\sqrt{3}}{2}} & 1 & 0 & -1 & 0 \\\hline {\cos} & 1 & {\frac{\sqrt{3}}{2}} & {\frac{\sqrt{2}}{2}} & {\frac{1}{2}} & 0 & -1 & 0 & 1\\\hline {\tan} & 0 & {\frac{\sqrt{3}}{3}} & 1 & {\sqrt{3}} & - & 0 & - & 0\\\hline {\cot} & - & {\sqrt{3}} & 1 & {\frac{\sqrt{3}}{3}} & 0 & - & 0 & -\\\hline \end{array}$$

To see how to use this table we will do some example tasks for you.

Example No. 1
\begin{align} & 2\sin(60^{\circ})-4\tan(30^{\circ})+3\cos(45^{\circ})= \\ & = 2\cdot \frac{\sqrt{3}}{2}-4\cdot \frac{\sqrt{3}}{3}+3\cdot \frac{\sqrt{2}}{2} \\ & = \frac{6\sqrt{3}}{6}-\frac{8\sqrt{3}}{6}+\frac{9\sqrt{2}}{6}=\frac{9\sqrt{2}-2\sqrt{3}}{6} \end{align}

Example No. 2
\begin{align} & \sin^2(60^{\circ})+2\cos^2(30^{\circ})-3\tan^2(60^{\circ})= \\ & = \Bigl(\frac{\sqrt{3}}{2}\Bigr)^2+2\cdot \Bigl(\frac{\sqrt{3}}{2}\Bigr)^2-3\cdot ({\sqrt{3}})^2 \\ & = \frac{3}{4}+\frac{3}{2}-9=-6.75 \end{align}

Note! To calculate exact values of the trigonometric expressions we can use calculator with trigonometric functions. This table is helpful when using of calculator is not allowed.

2019-03-03