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Geometry & MeasuresStudy Notes

Worked Example 2

Part of Exact Trig Values — GCSE Mathematics

This study notes covers Worked Example 2 within Exact Trig Values for GCSE Mathematics. Revise Exact Trig Values in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 4 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 5 of 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 6

Practice

14 questions

Recall

4 flashcards

Worked Example 2

Find the exact value of 2 sin 45° cos 45°.

Solution

From the exact values table:

sin 45° = √2/2

cos 45° = √2/2

2 sin 45° cos 45° = 2 × (√2/2) × (√2/2)

= 2 × (√2 × √2)/(2 × 2)

= 2 × 2/4

= 4/4 = 1

Keep building this topic

Read this section alongside the surrounding pages in Exact Trig Values. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 1Worked Example 3The Special TrianglesThe Values You MUST Know

Practice Questions for Exact Trig Values

What is the exact value of sin 30°?

  • A. √3/2
  • B. 1/2
  • C. √2/2
  • D. 1
1 markfoundation

James says that sin 30° and cos 60° are equal. Is James correct? Explain your answer using exact values.

2 marksstandard

Quick Recall Flashcards

Sin Pattern
sin 0°=0, sin 30°=1/2, sin 45°=√2/2, sin 60°=√3/2, sin 90°=1. Pattern: √n/2 for n=0,1,2,3,4
Cos Pattern
Cos is sin BACKWARDS. cos θ = sin(90°-θ). So cos 30° = sin 60°, etc.

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Worked Example 1

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Worked Example 3