Watch out
Forgetting the square on sine or cosine.
Scottish National 5 Mathematics
National 5 Maths Trigonometric identities
Use the two National 5 identities to find values and simplify expressions.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Choose the identity containing the known value and target value.
- Decide whether a calculator supports the method; exact working may still be required.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Trigonometric identities is an assessed part of Scottish National 5 Mathematics in the trigonometry area. Use the two National 5 identities to find values and simplify expressions.
Choose the identity containing the known value and target value.
Substitute before rearranging.
Use the stated angle range to choose a positive or negative root where needed.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- sin² x + cos² x = 1
- tan x =
Check
Substitute the known values into the identity; for an acute angle, sine and cosine should both be positive.
Exam tip
Show the selected relationship and substitution before calculating, then give every required angle or unit.
Worked examples
Worked example 1
Trigonometric identities worked example
Given cos x = and x is acute, find sin x
- sin² x = 1 − =
- x is acute, so sin x is positive.
Answer: sin x =
Watch out
- Forgetting the square on sine or cosine.
- Choosing the wrong sign without using the angle range.