Chapter 6. Trigonometry

Right-triangle ratios. For an acute angle θ: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent (mnemonic: SOH-CAH-TOA) [3][4].

Special angles

Radians. 180° = π radians. Arc length s = rθ when θ is in radians.

Unit circle. For a point on the unit circle at angle θ, (x, y) = (cos θ, sin θ).

Key identities

sin²θ + cos²θ = 1

tan θ = sin θ / cos θ

sin(A + B) = sin A cos B + cos A sin B

cos(A + B) = cos A cos B − sin A sin B

sin 2θ = 2 sin θ cos θ

Laws for any triangle (sides a, b, c opposite angles A, B, C):

Law of sines: a/sin A = b/sin B = c/sin C

Law of cosines: c² = a² + b² − 2ab cos C

Graphs. y = sin x and y = cos x have period 2π and amplitude 1.

Review: A ladder 10 m long makes a 60° angle with the ground. How high does it reach? (Answer: 10 sin 60° ≈ 8.66 m.)