- A-Level Maths

# Trigonometry

The graphs of sin, cos and tan are **periodic** - this means they repeat themselves for certain intervals.

Both y = sinθ and y = cosθ have a repeating period of 360° or 2π

Both y = sinθ and y = cosθ have a a maximum value of 1 and a minimum of -1

y = sinθ and y = cosθ are the same shape, but offset by 90° or 1/2π.

y=tanθ or 1π. repeats every 180° or 1π.

There are vertical asymptotes at 90° and then every 180° after in each direction. This means tanθ is undefined at these values.

Standard graph transformations apply to trigonometric graphs. See notes sheet on Functions, Graphs & Transformations

## Sine & Cosine Rules

Often you will only know some side lengths or angles in a triangle, and will need to work out the missing measurements. When you know two side lengths and one of their corresponding (opposite) angles or vice versa, use the **sine rule:**

Sometimes the sine rule produces two possible solutions for a missing angle, an acute angle and an obtuse angle. Make sure you get the right one.

### Cosine Rule

If you know just the three side lengths and no angles, use the **cosine rule**: