# S-Cool Revision Summary

## S-Cool Revision Summary

#### The Basics from GCSE

Use Pythagoras and Trigonometry in right-angled triangles

Use Sine and Cosine rules in non-right-angled triangles

2p radians = 360 degrees, arc length s = rq, area of a sector A = Angles on a coordinate grid are measured anticlockwise from the +ve x-axis.

 The trig. functions are positive in these zones: Use these zones to find the extra solutions to trig. equations. Solve trig equations by: Finding the first solution using a calculator Finding the second solution using the grid General solutions are found by adding: 2np or 3600 for sin and cos. np or 1800 for tan Remember the period changes with multiples of q. Cos cq has period #### Graphs of sin, cos and tan   #### Identities (In order of usefulness)

1. tan q = 2. cos2 q + sin2 q = 1

3. sec x = , cosec x = and cot x = .

#### Double Angle Formulae

1. sin 2A = 2sin A cos A,

2. cos 2A = cos2 A - sin2 A = 1 - 2sin2 A = 2cos2 A - 1

3. These came from the compound angle formulae:

1. sin (A + B) = sin A cos B + cos A sin B

2. sin (A - B) = sin A cos B - cos A sin B

3. cos (A + B) = cos A cos B - sin A sin B

4. cos (A - B) = cos A cos B + sin A sin B R cos (q - a) is used to add sine and cosine functions together.

(i.e. acosq + bsinq = R cos (q - a)) and R and a are found by:

1. Expand the bracket

2. Match the question to the expansion

3. Find R and a using R = , and a = Sometimes you may need the factor formulae (adding sines or cosines together) or the half-angle formulae when integrating. 