Maths for electricians · Topic 5 of 6
Trigonometry: sin, cos and tan
Trigonometry links the angles of a right-angled triangle to its sides. At Level 2 you mostly need the basics; it matters more at Level 3, where power factor is a cosine.
- P – Power
SOH CAH TOA
Label the sides from the angle θ you're using (see the triangle in Pythagoras' theorem): the opposite is across from it, the adjacent is next to it, and the hypotenuse is the longest side.
| Memory aid | Formula |
|---|---|
| SOH | sin θ = opposite ÷ hypotenuse |
| CAH | cos θ = adjacent ÷ hypotenuse |
| TOA | tan θ = opposite ÷ adjacent |
Why ladders lean at 75°
The 1-in-4 rule puts the foot 1 unit out for every 4 up. The height is opposite the angle at the ground and the distance out is adjacent, so tan θ = 4 ÷ 1 = 4. Using the inverse key, θ = tan⁻¹(4) = 75.96°, which is where the 75° figure comes from.
Finding a side
A cable tray rises at 30° along a 10 m sloping run. How much height does it gain? Height is opposite, the run is the hypotenuse, so height = 10 × sin 30° = 10 × 0.5 = 5 m.
Power factor (Level 3 preview)
In the power triangle, the angle φ between true power P and apparent power S gives the power factor: pf = cos φ = P ÷ S. A motor using 4 kW from 5 kVA has a power factor of 4 ÷ 5 = 0.8.
Exam tip: make sure your calculator is in degrees (D or DEG on the screen). In radians, sin 30 gives −0.99 instead of 0.5.
Try it: Power and current calculator (power factor)
Mini test
Pick an answer to see if you're right and why.