Question

Find one positive and one negative angle co-terminal with an angle of 9π/6.

Answer 1

To find co-terminal angles for 9π/6, first simplify to 3π/2. A positive co-terminal angle is found by adding 2π, resulting in 7π/2. A negative co-terminal angle is found by subtracting 2π, resulting in -1π/2.

Step-by-step explanation:

To find one positive and one negative angle co-terminal with an angle of 9π/6, we recall that co-terminal angles are angles that share the same initial and terminal sides but differ in the number of full rotations they make around the circle. One full rotation is 2π radians (or 360°).

First, simplify the given angle: 9π/6 = 3π/2.

For a positive co-terminal angle, add 2π to the given angle:
3π/2 + 2π = 3π/2 + 4π/2 = 7π/2.

For a negative co-terminal angle, subtract 2π from the given angle:
3π/2 - 2π = 3π/2 - 4π/2 = -1π/2.

Therefore, the positive co-terminal angle is 7π/2 and the negative co-terminal angle is -1π/2.