Mathslive.ie

TRIGONOMETRY

Exam Cog
①SOH CAH TOA

sin = O/H   cos = A/H   tan = O/A

Hyp: opposite the right angle. Opp: across from A. Adj: beside A.

★ Silly Old Harry, Caught A Herring, Trawling Off America
②FINDING A SIDE
  1. Label opp / adj / hyp
  2. Pick the ratio with your two sides
  3. Solve for the unknown

On top → multiply.   On bottom → divide.

③FINDING AN ANGLE

Know two sides → make the ratio

A = sin⁻¹ / cos⁻¹ / tan⁻¹ of it

⚠ Calculator must be in DEGREES.
④ELEVATION & DEPRESSION

Elevation: up from the horizontal

Depression: down from the horizontal

★ Depression = the angle looking back up (alternate)
⑤SPECIAL VALUES

sin30 = 0.5   cos60 = 0.5

tan45 = 1   tan60 = √3

1° = 60′

⑥PYTHAGORAS

hyp² = opp² + adj²

Use it when you have two sides and no angle.

⑦METHOD
  1. Draw & label the triangle
  2. Mark the angle and the sides you know
  3. Choose SOH, CAH or TOA
  4. Round as asked; state units
⑧VOCAB

Horizontal flat   Vertical upright

Opposite faces the angle

⑨WATCH-OUTS
⚠ Only works in a RIGHT-angled triangle. No right angle? Split it or use Pythagoras.