Trigonometry connects angles to side ratios in right triangles — and powers everything from architecture to GPS.
Drag around the circle
θ = 30° = π/6
quadrant I
sin θ = y = 0.5
cos θ = x = 0.866
tan θ = sin/cos = 0.577
The three ratios (right triangle)
'Opp' and 'adj' are taken relative to the angle θ.
Your turn
A ramp rises 1 m over a 4 m horizontal run. What's the angle of incline?
Trig turns 'I can't reach it' into 'I can measure it': the height of a mountain, the distance to a star, the position from GPS satellites — all from angles and ratios.
Three ratios
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
- tan θ = opposite / adjacent