Worked example 1
Find an exact value
Find sin 75° exactly using an addition formula.
- Write 75° = 45° + 30°
- Use sin(A + B).
- Substitute the exact values and simplify.
Answer: sin 75° =
Higher Mathematics
Higher Maths Addition and double-angle formulae
Practise addition and double-angle formulae for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Apply addition formulae, double-angle formulae and related identities to simplify or solve.
Before you start
- Know exact trig values.
- Expand brackets accurately.
- Use the Pythagorean identity.
Explanation
Addition formulae expand trigonometric functions of sums and differences. Substituting the same angle gives the double-angle formulae.
Higher questions may combine these formulae with identities or equations, so state the chosen formula first.
Method and rules
- sin(A ± B) = sin A cos B ± cos A sin B
- cos(A ± B) = cos A cos B −/+ sin A sin B
- sin 2x = 2 sin x cos x; cos 2x = cos² x − sin² x
Worked examples
Worked example 2
Method check
State sin 2x.
- It follows from sin(x + x)
So: 2 sin x cos x.
Watch out
- Using the cosine sign pattern for sine.
- Changing both signs in cos(A − B)
- Rounding exact values before simplifying.
Exam reminder
For addition and double angle formulae, show the defining equation or formula before simplifying. Check that every final value satisfies the original restrictions, interval or context.
Related Higher Maths topics
Continue with the methods that connect most closely to this topic.