Revise: Trigonometry

radians = degrees × (π/180).

150° = 5π/6 radians.

s = rθ (θ in radians).

r=8, θ=2 → s=16.

SOH-CAH-TOA: sinθ=opp/hyp, cosθ=adj/hyp, tanθ=opp/adj.

opp=3,adj=4,hyp=5 → sinθ=3/5.

sin²θ + cos²θ = 1.

sinθ=3/5 → cosθ=4/5.

Exact values for 0°,30°,45°,60°,90° from special right triangles.

sin30°=1/2, cos30°=√3/2.

Standard position: vertex at origin, initial side on positive x-axis.

400° is coterminal with 40°.

360° = 2π radians; a radian is where arc length = radius.

π/3 rad = 60°.

s = rθ, only with θ in radians.

r=6, θ=1.5 → s=9.

A = (1/2)r²θ — a sector is the θ/2π fraction of the full circle.

r=10, θ=π/3 → A≈52.4.

Six ratios from opp/adj/hyp; the same for all similar right triangles.

opp=6,adj=8,hyp=10 → cosθ=0.8.

sin²θ+cos²θ=1; tanθ=sinθ/cosθ.

cosθ=12/13 → sinθ=5/13.

Derive from 45-45-90 and 30-60-90 triangles; 30°/60° values swap.

tan45°=1.

One side + one other measurement solves the whole triangle.

∠C=35°, hyp=10 → AB≈5.74, BC≈8.19, ∠A=55°.

Elevation: up from horizontal. Depression: down from horizontal. Equal by alternate angles.

40m away, 32° elevation → height≈25m.