Trigonometry and Modelling:

Addition formulae:

Proving addition formulae using geometry:

a) Using triangle ADE:

DE=sin(a + b)

AD= cos(a + b)

DE=DF+FE

sin(a + b) = sinacosb + cosasinb as required

b) AD=AB-DB

cos(a + b) = cosacosb - sinasinb as required

‘Show that’ questions using addition formulae:

Proving expressions using addition formulae:

‘Given that’ questions using addition formulae:

Using addition formulae to find exact values of trigonometric functions of different angles:

‘Given that’ questions using addition formulae to find exact solutions:

Double angle formulae: (best to learn these!)

Use the double-angle formulae to write each of the following as a single trigonometric ratio:

Use the double-angle formulae to write each of the following as a single trigonometric ratio:

Use the double-angle formulae to write each of the following as a single trigonometric ratio:

Using the double-angle formulae in expressions:

Finding exact values using double-angle formulae:

Using the addition formulae to solve trigonometric equations:

Using the double-angle formulae to solve trigonometric equations:

More examples of questions that could appear:

More examples of questions that could appear:

Simplifying acosx±bsinx

Examples of simplifying acosx±bsinx

Including graphs:

Solving graphs with the simplification:

Maximum values using simplification:

Proving trigonometric identities:

Modelling with trigonometric equations:

Example question of modelling with trigonometric equations:

d)

11.5-0.5sin(t-2)=11.3

-0.5sin(t-2)=-0.2

sin(t-2)=0.4

t-2=-3.553…, 0.4115…, 2.73…, 6.6947…

t=2.41 hours, 4.73 hours.

t=2 h 25 min, 4 h 44 min