Trigonometry · SEC2_GYM

Trigonometric identities

Question 1/8+12 XP
Simplify .
Unit circleθ = 60° = π/3
-1-0.50.51-1-0.50.51xy
Read off
true for every angle
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) = (0.500, 0.866). 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.