For a right triangle with angle θ: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Reciprocals: cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ. These ratios depend only on the angle, not the size of the triangle.

Key values: sin 0°=0, sin 30°=½, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1. cos is reverse of sin. tan 0°=0, tan 30°=1/√3, tan 45°=1, tan 60°=√3, tan 90°=undefined. Memorise using the table — it is essential for all trigonometry problems.

Three fundamental identities: (1) sin²θ + cos²θ = 1. (2) 1 + tan²θ = sec²θ. (3) 1 + cot²θ = cosec²θ. These are used to simplify expressions and prove other identities. All three can be derived from the Pythagorean theorem.

The three fundamental identities: (1) sin²θ + cos²θ = 1 (Pythagorean identity); (2) 1 + tan²θ = sec²θ; (3) 1 + cot²θ = cosec²θ. These are derived directly from the definitions using the Pythagorean theorem. To prove a trigonometric identity, start with the more complex side and simplify step-by-step to reach the other side. Never move terms across the = sign (it is an identity, not an equation to solve). Common technique: convert everything to sin and cos and simplify.