Question

Find the nearest two positive co-terminal angles and nearest two negative co-terminal angles of -π/3.

Answer 1

The nearest positive co-terminal angles of -π/3 are 5π/3 and 11π/3, and the nearest negative co-terminal angles are -7π/3 and -13π/3.

Step-by-step explanation:

To find the nearest positive co-terminal angles and nearest negative co-terminal angles of -π/3, we will add and subtract multiples of 2π, which is the angular distance of one complete circle. Since angles defined in the counter clockwise direction are positive, adding 2π will give us the nearest positive co-terminal angle, and subtracting 2π from the angle will give us the nearest negative co-terminal angle.

For the nearest positive co-terminal angles:

1. -π/3 + 2π = 5π/3
2. -π/3 + 4π = 11π/3

For the nearest negative co-terminal angles:

1. -π/3 - 2π = -7π/3
2. -π/3 - 4π = -13π/3