SEC2_GYM · Trigonometry · TRIG.IDENTITIES

Trigonometric identities

Intuition

Understand first, compress later.

Trigonometry connects angles with side ratios and periodic motion.

Switch representations

Unit circleθ = 30° = π/6

radius = 1cos θ (horizontal)sin θ (vertical)angle θpoint P(cos θ, sin θ)

Point P on the unit circle has coordinates (cos θ, sin θ) = (0.866, 0.500). The cosine is the horizontal leg and the sine the vertical one; since the radius is 1, Pythagoras gives cos²θ + sin²θ = 1. That is why both values always stay between −1 and 1.

Formal view

You can trigonometric identities when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.