What are the terminal points determined by π/2, π, -π/2, and 2π?

Solution:

Let us consider a unit circle ( a circle with radius r = 1) with center ‘o’.

The rays originating from the origin (center of the circle) and terminating on the circle are shown below:

The ray OA = OP = r = radius of the circle = 1.

At point P(x, y)

OE = rcosθ = x and OP = rsinθ = y, Since r = 1

The Terminal point P at θ = (cosθ, sinθ)

Similarly the terminal point B at π/2 is represented as (rCosπ/2, rSinπ/2) and since r = 1.

The terminal point B is (0, 1).

Terminal Point C at π = (rcosπ, rsinπ) = (1cosπ, 1sinπ) = (-1, 0)

Terminal Point D -at - π/2 = (rcos-π/2, rsin-π/2) = (1cos -π/2, 1sin -π/2) = (0, -1)

Terminal Point A at 2π = (rcos2π, rsin2π) = (1cos2π, 1sin2π) = (1, 0)

What are the terminal points determined by π/2, π, -π/2, and 2π?

Summary:

The terminal points determined by π/2, π, -π/2, and 2π are (0, 1), (-1, 0), (0, -1), and (1, 0)