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

Radians

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.

trig functions

Solve trig equations by:

  1. Finding the first solution using a calculator

  2. 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

Sine
Cosine
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

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.