Question

Use patterns to find the values of sin 30° and cos 30° and then compare their values.

Answer 1

A quick pattern/geometry method: start with an equilateral triangle of side length 2. Drop an altitude — it splits the triangle into two congruent 30°–60°–90° right triangles. In one right triangle:

- hypotenuse = 2
- short leg (opposite 30°) = 1
- long leg (opposite 60°) = √(2^2 − 1^2) = √3

So for 30°,
- sin 30° = (opposite)/(hypotenuse) = 1/2,
- cos 30° = (adjacent)/(hypotenuse) = √3/2 ≈ 0.866.

Comparison: cos 30° = √3/2 ≈ 0.866 is greater than sin 30° = 1/2 = 0.5. (Also note cos 30° = sin 60°.)