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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: