Chapter 11: Trigonometry

Trigonometry introduces the six trigonometric ratios defined from a right triangle's sides, their exact values at 0°, 30°, 45°, 60° and 90°, complementary-angle relationships, and the fundamental identities. In a 30-60-90 triangle, sin30° is always exactly 1/2, regardless of how large or small the actual triangle is.

Mixing up which side is opposite versus adjacent — especially when a triangle is drawn at an unfamiliar angle — causes most of the errors here, along with misremembering an identity's exact form under pressure (sin²θ+cos²θ=1 is the one most often garbled). Every ratio here only stays consistent because of the similar-triangles reasoning from the previous chapter.