This study notes covers Worked Example 3 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 6 of 7 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 3
Show that sin²30° + cos²30° = 1.
Solution
From the exact values table:
sin 30° = 1/2, so sin²30° = (1/2)² = 1/4
cos 30° = √3/2, so cos²30° = (√3/2)² = 3/4
sin²30° + cos²30° = 1/4 + 3/4
= 4/4 = 1 ✓
This confirms the trig identity sin²θ + cos²θ = 1
Practice questions for Exact Trig Values
What is the exact value of sin 30°?
James says that sin 30° and cos 60° are equal. Is James correct? Explain your answer using exact values.