Trigonometry Sheet 3

ASTC Quadrant Formulas (All 78 Results)

ASTC Rule: Q1 (All +ve) | Q2 (Sin/Cosec +ve) | Q3 (Tan/Cot +ve) | Q4 (Cos/Sec +ve)

1. Vertical Axis: $$90^\circ$$&$$270^\circ$$ (Ratios Change)

$$\sin \leftrightarrow \cos$$, $$\tan \leftrightarrow \cot$$, $$\sec \leftrightarrow \csc$$

Angle (θ)	$$\sin$$	$$\cos$$	$$\tan$$	$$\csc$$	$$\sec$$	$$\cot$$
$$90^\circ – \theta$$ (Q1)	$$\cos\theta$$	$$\sin\theta$$	$$\cot\theta$$	$$\sec\theta$$	$$\csc\theta$$	$$\tan\theta$$
$$90^\circ + \theta$$ (Q2)	$$\cos\theta$$	$$-\sin\theta$$	$$-\cot\theta$$	$$\sec\theta$$	$$-\csc\theta$$	$$-\tan\theta$$
$$270^\circ – \theta$$ (Q3)	$$-\cos\theta$$	$$-\sin\theta$$	$$\cot\theta$$	$$-\sec\theta$$	$$-\csc\theta$$	$$\tan\theta$$
$$270^\circ + \theta$$ (Q4)	$$-\cos\theta$$	$$\sin\theta$$	$$-\cot\theta$$	$$-\sec\theta$$	$$\csc\theta$$	$$-\tan\theta$$

2. Horizontal Axis & Periodicity (Ratios Remain Same)

Angle (θ)	$$\sin$$	$$\cos$$	$$\tan$$	$$\csc$$	$$\sec$$	$$\cot$$
$$180^\circ – \theta$$ (Q2)	$$\sin\theta$$	$$-\cos\theta$$	$$-\tan\theta$$	$$\csc\theta$$	$$-\sec\theta$$	$$-\cot\theta$$
$$180^\circ + \theta$$ (Q3)	$$-\sin\theta$$	$$-\cos\theta$$	$$\tan\theta$$	$$-\csc\theta$$	$$-\sec\theta$$	$$\cot\theta$$
$$360^\circ – \theta$$ (Q4)	$$-\sin\theta$$	$$\cos\theta$$	$$-\tan\theta$$	$$-\csc\theta$$	$$\sec\theta$$	$$-\cot\theta$$
$$360^\circ + \theta$$ (Q1)	$$\sin\theta$$	$$\cos\theta$$	$$\tan\theta$$	$$\csc\theta$$	$$\sec\theta$$	$$\cot\theta$$
$$2n\pi + \theta$$ (Q1)	$$\sin\theta$$	$$\cos\theta$$	$$\tan\theta$$	$$\csc\theta$$	$$\sec\theta$$	$$\cot\theta$$
$$2n\pi – \theta$$ (Q4)	$$-\sin\theta$$	$$\cos\theta$$	$$-\tan\theta$$	$$-\csc\theta$$	$$\sec\theta$$	$$-\cot\theta$$
$$-2n\pi + \theta$$ (Q1)	$$\sin\theta$$	$$\cos\theta$$	$$\tan\theta$$	$$\csc\theta$$	$$\sec\theta$$	$$\cot\theta$$
$$-2n\pi – \theta$$ (Q4)	$$-\sin\theta$$	$$\cos\theta$$	$$-\tan\theta$$	$$-\csc\theta$$	$$\sec\theta$$	$$-\cot\theta$$
$$-\theta$$ (Q4)	$$-\sin\theta$$	$$\cos\theta$$	$$-\tan\theta$$	$$-\csc\theta$$	$$\sec\theta$$	$$-\cot\theta$$