Trigonometric Functions — Chapter Summary

Angle is a measure of rotation

Angle is a measure of rotation of a ray about its initial point. The initial ray, terminal side, and vertex describe the angle. Anticlockwise rotation

One degree is one 360th

One degree is one 360th of a revolution. A degree is divided into 60 minutes and a minute into 60 seconds. One complete revolution equals 2π radians,

In a circle of radius r

In a circle of radius r, an arc of length l subtends an angle θ at the centre, where l = rθ. This formula directly connects geometry with radian measu

For a point P(a

For a point P(a, b) on the unit circle with angle AOP = x radian, define cos x = a and sin x = b. Since P lies on the unit circle, cos²x + sin²x = 1.

Angles that are integral multiples

Angles that are integral multiples of π/2 are quadrantal angles. At these angles, the unit circle gives exact values such as cos 0 = 1, sin 0 = 0, cos