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SQA National 5 Mathematics

Exact values

Using exact trig values for 0, 30, 45, 60 and 90 degrees.

Formula referenceMixed revision

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

  • Read the command word and identify what is being asked.
  • Write down the relevant formula, rule or algebraic structure before substituting values.
  • Keep working set out line by line so method marks are clear.
National 5 Mathematics lesson

Explanation

Exact values is part of Trigonometry in SQA National 5 Mathematics. The key skill is choosing a method and communicating the working clearly.

For exact values, underline the values or algebraic terms you are given, choose the matching rule, then simplify one line at a time.

National 5 answers should show enough working for a marker to follow the method. Exact answers are expected where the question asks for exact form; otherwise round only at the end.

Key formulae and rules

  • Usually non-calculator.
  • SOH CAH TOA, sine rule, cosine rule and Area = 12 ab sin C as needed

Watch out

Choosing a method from a remembered keyword instead of reading the whole question.

Check

Check your answer against the diagram. The longest side should still be opposite the largest angle.

Exam tip

Method marks come from clear setup and correct mathematical notation, not just a final answer.

Calculator tip

Make sure the calculator is in degree mode before using sin, cos, tan or inverse trig.

Worked examples

Worked example 1

Choose a trig rule

A right-angled triangle has angle 40 degrees, opposite side x and hypotenuse 12 cm.

  1. Opposite and hypotenuse use sine.
  2. sin 40 = x / 12
  3. x = 12 sin 40

Answer: x = 7.7 cm to 1 decimal place

Worked example 2

Use an inverse trig function

Find θ when opposite = 5 and adjacent = 9.

  1. Use tan because opposite and adjacent are involved.
  2. tan θ = 5 / 9
  3. θ = tan−1(5 / 9)

So: θ = 29.1 degrees

Worked example 3

Check triangle type

A non-right-angled triangle has sides 7 cm and 10 cm with included angle 50 degrees.

  1. This is not SOH CAH TOA.
  2. SAS information points to cosine rule.

Answer: Use cosine rule.

Watch out

  • Choosing a method from a remembered keyword instead of reading the whole question.
  • Dropping negative signs, powers or brackets during the working.
  • Giving a rounded decimal when an exact answer or algebraic form is needed.