In this post we are going to provide you the values of some of trigonometric ratios like \(\;\sin x \;\) , \(\;\cos x \;\) and \(\;\tan x \;\) on some angles.
Here are two tables, in first table angles are in degree, and in second table angles are in radian.
\[\begin{array}{|c|c|c|c|} \hline \theta & \sin \theta & \cos \theta & \tan \theta \\ \hline 0^{\circ} & 0 & 1 & 0 \\ \hline 15^{\circ} & \displaystyle \frac{\sqrt{6}-\sqrt{2}}{4} & \displaystyle \frac{\sqrt{6}+\sqrt{2}}{4} & 2-\sqrt{3} \\ \hline 18^{\circ} & \displaystyle \frac{\sqrt{5}-1}{4} & \displaystyle \frac{\sqrt{10+2 \sqrt{5}}}{4} & \sqrt{\displaystyle \frac{5-2 \sqrt{5}}{5}} \\ \hline 30^{\circ} & \displaystyle \frac{{1}}{2} & \displaystyle \frac{\sqrt{3}}{2} & \displaystyle \frac{1}{\sqrt{3}} \\ \hline 36^{\circ} & \displaystyle \frac{\sqrt{10-2 \sqrt{5}}}{4} & \displaystyle \frac{\sqrt{5}+1}{4} & \displaystyle \frac{\sqrt{10-2 \sqrt{5}}}{\sqrt{5}+1} \\ \hline 45^{\circ} & \displaystyle \frac{1}{\sqrt{2}} & \displaystyle \frac{1}{\sqrt{2}} & 1 \\ \hline 54^{\circ} & \displaystyle \frac{\sqrt{5}+1}{4} & \displaystyle \frac{\sqrt{10-2 \sqrt{5}}}{4} & \displaystyle \frac{\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}} \\ \hline 60^{\circ} & \displaystyle \frac{\sqrt{3}}{2} & \displaystyle \frac{1}{2} & \sqrt{3} \\ \hline 72^{\circ} & \displaystyle \frac{\sqrt{10+2 \sqrt{5}}}{4} & \displaystyle \frac{\sqrt{5}-1}{4} & \sqrt{5+2 \sqrt{5}} \\ \hline 75^{\circ} & \displaystyle \frac{\sqrt{6}+\sqrt{2}}{4} & \displaystyle \frac{\sqrt{6}-\sqrt{2}}{4} & 2+\sqrt{3}\\ \hline 90^{\circ} & 1 & 0 & \infty \\ \hline 120^{\circ} & \displaystyle \frac{\sqrt{3}}{2} & - \displaystyle \frac{1}{2}& -\sqrt{3} \\ \hline 180^{\circ} & 0 & -1 & 0 \\ \hline 270^{\circ} & -1 & 0 & \infty \\ \hline 360^{\circ} & 0 & 1 & 0 \\ \hline \end{array}\]
\[\begin{array}{|c|c|c|c|} \hline \theta \;\text{in} \;\operatorname{rad} & \sin \theta & \cos \theta & \tan \theta \\ \hline 0 & 0 & 1 & 0 \\ \hline \displaystyle \frac{\pi}{12} & \displaystyle \frac{\sqrt{6}-\sqrt{2}}{4} & \displaystyle \frac{\sqrt{6}+\sqrt{2}}{4} & 2-\sqrt{3} \\ \hline \displaystyle \frac{\pi}{10} & \displaystyle \frac{\sqrt{5}-1}{4} & \displaystyle \frac{\sqrt{10+2 \sqrt{5}}}{4} & \sqrt{\displaystyle \frac{5-2 \sqrt{5}}{5}} \\ \hline \displaystyle \frac{\pi}{6} & \displaystyle \frac{1}{2} & \displaystyle \frac{\sqrt{3}}{2} & \displaystyle \frac{1}{\sqrt{3}} \\ \hline \displaystyle \frac{\pi}{5} & \displaystyle \frac{\sqrt{10-2 \sqrt{5}}}{4} & \displaystyle \frac{\sqrt{5}+1}{4} & \displaystyle \frac{\sqrt{10-2 \sqrt{5}}}{\sqrt{5}+1} \\ \hline \displaystyle \frac{\pi}{4} & \displaystyle \frac{1}{\sqrt{2}} & \displaystyle \frac{1}{\sqrt{2}} & 1 \\ \hline \displaystyle \frac{3 \pi}{10} & \displaystyle \frac{\sqrt{5}+1}{4} & \displaystyle \frac{\sqrt{10-2 \sqrt{5}}}{4} & \displaystyle \frac{\sqrt{5}+1}{\sqrt{10-2 \sqrt{5}}} \\ \hline \displaystyle \frac{\pi}{3} & \displaystyle \frac{\sqrt{3}}{2} & \displaystyle \frac{1}{2} & \sqrt{3} \\ \hline \displaystyle \frac{2 \pi}{5} & \displaystyle \frac{\sqrt{10+2 \sqrt{5}}}{4} & \displaystyle \frac{\sqrt{5}-1}{4} & \sqrt{5+2 \sqrt{5}} \\ \hline \displaystyle \frac{5 \pi}{12} & \displaystyle \frac{\sqrt{6}+\sqrt{2}}{4} & \displaystyle \frac{\sqrt{6}-\sqrt{2}}{4} & 2+\sqrt{3}\\ \hline \displaystyle \frac{\pi}{2} & 1 & 0 & \infty \\ \hline \displaystyle \frac{2 \pi}{3} & \displaystyle \frac{\sqrt{3}}{2} & - \displaystyle \frac{1}{2}& -\sqrt{3} \\ \hline \pi & 0 & -1 & 0 \\ \hline \displaystyle \frac{3 \pi}{2} & -1 & 0 & \infty \\ \hline 2 \pi & 0 & 1 & 0 \\ \hline \end{array}\]
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