M4.3.6 For the adult
Exact values
On a calculator sin 45° shows 0.7071067812 and goes on. Is there a neat exact way to write it?
What this chapter teaches
Half a square (sides 1, 1, √2) and half an equilateral triangle (sides 1, √3, 2) give the exact values of sin, cos and tan for 30°, 45° and 60°. The learner can rebuild the table from these two sketches, and use the exact values to keep an answer in surd form.
Three questions to ask
There is no one right wording. Listen for the idea.
- How do you get the sides 1, √3 and 2 from an equilateral triangle?
- Why does half a square give tan 45° = 1?
- Why are 1 ÷ √2 and √2 ÷ 2 the same number?
After the chapter, the learner can
- Recall sin, cos and tan of 30°, 45° and 60°
- Work out those values from two special triangles
What they copy into their notebook
Half a square gives 45°: sides 1, 1, √2. Half an equilateral triangle gives 30° and 60°: sides 1, √3, 2. Read sin, cos and tan from these.