# Effect of Adding/Subtracting Angles on Trignometric Ratios

Following is the manner in which trigonometric ratios are affected when adding/subtracting angles:

Anglessincostancosecseccot
90°-θ$$\cos\theta$$$$\sin\theta$$$$\cot\theta$$$$\sec\theta$$cosec $$\theta$$$$\tan\theta$$
90°+θ$$\cos\theta$$$$-\sin\theta$$$$-\cot\theta$$$$\sec\theta$$$$-$$cosec $$\theta$$$$-\tan\theta$$
180°-θ$$\sin\theta$$$$-\cos\theta$$$$-\tan\theta$$cosec $$\theta$$$$-\sec\theta$$$$-\cot\theta$$
180°+θ$$-\sin\theta$$$$-\cos\theta$$$$\tan\theta$$$$-$$cosec $$\theta$$$$-\sec\theta$$$$\cot\theta$$
270°-θ$$-\cos\theta$$$$-\sin\theta$$$$\cot\theta$$$$-\sec\theta$$$$-$$cosec $$\theta$$$$\tan\theta$$
270°+θ$$-\cos\theta$$$$\sin\theta$$$$-\cot\theta$$$$-\sec\theta$$cosec $$\theta$$$$-\tan\theta$$
360°-θ$$-\sin\theta$$$$\cos\theta$$$$-\tan\theta$$$$-$$cosec $$\theta$$$$\sec\theta$$$$-\cot\theta$$
360°+θ$$\sin\theta$$$$\cos\theta$$$$\tan\theta$$cosec $$\theta$$$$\sec\theta$$$$\cot\theta$$
Please note that in all above formulae $$0\leqslant \theta \leqslant 90$$°

Also, for all values of θ:
 $$\sin(-\theta)=-\sin(\theta)$$ $$\cos(-\theta)=\cos(\theta)$$ $$\tan(-\theta)=-\tan(\theta)$$ cosec $$(-\theta)=-$$ cosec $$(\theta)$$ $$\sec(-\theta)=\sec(\theta)$$ $$\cot(-\theta)=-\cot(\theta)$$