Introduction to Trigonometry — Formula Sheet

sin A = BC/AC

cos A = AB/AC

tan A = BC/AB

cosec A = AC/BC = 1/sin A

sec A = AC/AB = 1/cos A

sin 0° = 0

cos 0° = 1

sin 90° = 1

cos 90° = 0

sin 45° = 1/√2

cos^2 A + sin^2 A = 1

1 + tan^2 A = sec^2 A

cot^2 A + 1 = cosec^2 A

cos A = √(1 - sin^2 A)

tan A = sin A / cos A

If tan A = 4/3, then sin A = 4/5, cos A = 3/5, cot A = 3/4, cosec A = 5/4, sec A = 5/3

If sin A = 1/3, then BC:AC = 1:3 and AB = 2√2 k

If AB = 29 and BC = 21 in a right triangle with right angle at C, then AC = 20

For that triangle, cos^2 θ + sin^2 θ = 1 and cos^2 θ - sin^2 θ = 41/841

sin A = BC/AC, cos A = AB/AC, tan A = BC/AB.

The fundamental identity is cos^2 A + sin^2 A = 1.

If tan A = 4/3, then the other ratios are sin A = 4/5, cos A = 3/5, cot A = 3/4, cosec A = 5/4, sec A = 5/3.

If AB = 29 and BC = 21 in a right triangle with right angle at C, then AC = 20.

cosec A = AC/BC, sec A = AC/AB, and cot A = AB/BC.

Also, cosec A = 1/sin A, sec A = 1/cos A, and cot A = 1/tan A.

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