Need to Know

Trigonometry

The trig ratios and rules you must have ready.

How to use this: say each rule in your head, then tap Show me to check.

SOH CAH TOA

2 rules

Rule 01

The three ratios

sin = O/H cos = A/H tan = O/A

Hyp is opposite the right angle; opp is across from the angle; adj is beside it.

Rule 02

Remember it

Silly Old Harry, Caught A Herring, Trawling Off America.

Finding a side

1 rule

Rule 03

Which way to solve

Unknown on top: multiply (e.g. x = 10·sin30). Unknown on the bottom: divide (e.g. x = 7 ÷ sin53).

Finding an angle

1 rule

Rule 04

Use the inverse

Know two sides ⇒ take the ratio, then sin⁻¹, cos⁻¹ or tan⁻¹ on the calculator.

Elevation & depression

1 rule

Rule 05

Which is which

Elevation up from the horizontal; depression down from the horizontal. The depression angle equals the angle looking back up (alternate angles).

Calculator & Pythagoras

1 rule

Rule 06

Two reminders

Calculator in degrees: sin35 ≈ 0.57. And 1° = 60′.

Right-angled triangle: hyp² = opp² + adj².

Mathslive.ie · Trigonometry · Need to Know