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# Reduction formulas

The trigonometric reduction formulas help us to reduce big angles in common sines, cosines, tangents and cotangents functions.

If we have $\frac{\pi}{2}$ or $\frac{3\pi}{2}$ angles in the reduction formula, the formula changes sine to cosine, cosine to sine, tangent to contingent, cotangent to tangent. If we have ${\pi}$ or ${2\pi}$ angles in the formula, the function does not change. Then we need to know the signs of the trigonometric functions in each quadrant.

$$\small{\begin{array}{|c|c|c|c|c|} \hline {\alpha} & \sin\alpha & \cos\alpha & \tan\alpha & \cot\alpha \\\hline {\frac{\pi}{2}-x} & +\cos\alpha & +\sin\alpha & +\cot\alpha & +\tan\alpha \\\hline {\frac{\pi}{2}+x} & +\cos\alpha & -\sin\alpha & -\cot\alpha & -\tan\alpha \\\hline {\pi-x} & +\sin\alpha & -\cos\alpha & -\tan\alpha & -\cot\alpha \\\hline {\pi+x} & -\sin\alpha & -\cos\alpha & +\tan\alpha & +\cot\alpha \\\hline {\frac{3\pi}{2}-x} & -\cos\alpha & -\sin\alpha & +\cot\alpha & +\tan\alpha \\\hline {\frac{3\pi}{2}+x} & -\cos\alpha & +\sin\alpha & -\cot\alpha & -\tan\alpha \\\hline {2\pi-x} & -\sin\alpha & +\cos\alpha & -\tan\alpha & -\cot\alpha \\\hline \end{array}}$$

2020-11-28

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