Trigonometry — Formula Sheet

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ = cos θ/sin θ

sin² θ + cos² θ = 1

1 + cot² θ = cosec² θ

1 + tan² θ = sec² θ

BC² + AB² = AC²

For the triangle in Fig. 6.2, sinθ = AB/AC, cosθ = BC/AC, and tanθ = AB/BC.

cosecθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ.

In the triangle form, cosecθ = hypotenuse/opposite side, secθ = hypotenuse/adjacent side, and cotθ = adjacent side/opposite side.

Identity II is sin²θ + cos²θ = 1.

Identity III is 1 + cot²θ = cosec²θ.

sinθ at 0°, 30°, 45°, 60°, 90° is 0, 1/2, 1/√2, √3/2, 1.

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

In a right triangle, sinθ = opposite side / hypotenuse, cosθ = adjacent side / hypotenuse, and tanθ = opposite side / adjacent side.

cosecθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ = cosθ/sinθ.

Also, sinθ × cosecθ = 1, cosθ × secθ = 1, and tanθ × cotθ = 1.

From the Pythagoras theorem in a right triangle, BC² + AB² = AC².

The key values for acute and special angles are

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