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• 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: