20.4 Exact trigonometric values — Practise with help
Try each problem first. Open a hint if you need it, then use the working to check your method.
Warm-up: remember
Answer these from memory. Do not look back at the section.
- Simplify .
- Work out .
Answers
- . 2. .
If an answer differs, revisit Section 7.6 for simplifying surds and Section 4.2 for adding fractions.
Practise with help
1. Give sin 30° exactly.
Hint
Use the special-value table.
Full working
sin 30° = 1/2.
2. Work out cos 45° exactly.
Hint
The 45° triangle has equal legs.
Full working
cos 45° = √2/2.
3. Work out sin 60° × cos 30° exactly.
Hint
Both values are √3/2.
Full working
(√3/2)(√3/2) = 3/4.
Before opening each full working, name the method and explain which measurements led you to choose it.