Signs of sine, cosine and tangent
The coordinate plane has four quadrants; a rotating point moving counterclockwise passes through quadrants I, II, III, IV. sin α is the ordinate of the point, so it is positive in quadrants I and II and negative in III and IV. cos α is the abscissa: positive in I and IV, negative in II and III. Since tan α = sin α : cos α, it is positive when sin and cos have the same sign (quadrants I and III) and negative when they differ (II and IV); cot α has the same sign. A large or negative angle is brought into the range 0 to 2π by adding or subtracting whole multiples of 2π (360°). For an angle given as a real number we compare it with π/2 ≈ 1.57, π ≈ 3.14, 3π/2 ≈ 4.71, 2π ≈ 6.28.
“Quadrant and sign”: two axes are drawn on the floor; the teacher names an angle, a student stands in the right quadrant and shows the signs of sin, cos, tan with hand signals (+ or −).