Introduction to Trigonometry

sin A = Opposite / Hypotenuse = BC/AC

cos A = Adjacent / Hypotenuse = AB/AC

tan A = Opposite / Adjacent = BC/AB = sin A / cos A

cosec A = 1/sin A = Hypotenuse / Opposite = AC/BC

sec A = 1/cos A = Hypotenuse / Adjacent = AC/AB

sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1

cos 0° = 1, cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2, cos 90° = 0

tan 0° = 0, tan 30° = 1/√3, tan 45° = 1, tan 60° = √3, tan 90° = Not Defined

sin²A + cos²A = 1

1 + tan²A = sec²A ⟹ sec²A − tan²A = 1

1 + cot²A = cosec²A ⟹ cosec²A − cot²A = 1

tan A = sin A / cos A and cot A = cos A / sin A

If sin A = p/q, then cos A = √(q²−p²)/q using sin²A + cos²A = 1

If tan A = a/b, draw right triangle with opposite = a, adjacent = b, hypotenuse = √(a²+b²)