Determining the Position of $-pi/2$ on the Unit Circle

To locate the position of $-\pi/2$ on the unit circle, we need to understand the unit circle itself. The circle has a radius of 1 and is centered at the origin (0,0).

1. Start from the positive x-axis and move counterclockwise.

2. A negative angle indicates a clockwise direction.

So, $-\pi/2$ means we move $\pi/2$ radians clockwise from the positive x-axis.

At $-\pi/2$ radians, the coordinates on the unit circle are given by:

$ (\cos(-\pi/2), \sin(-\pi/2)) $

Since $\cos(-\pi/2) = 0$ and $\sin(-\pi/2) = -1$, the position is:

$ (0, -1) $

To determine the location of $-pi/2$ radians on the unit circle, follow these steps:

1. Navigate in the clockwise direction as the angle is negative.

2. $-pi/2$ radians is equivalent to rotating $90^{circ}$ clockwise starting from the positive x-axis.

The coordinates at $-pi/2$ radians can be obtained using trigonometric functions:

$ (cos(-pi/2), sin(-pi/2)) $

The values are:

$ cos(-pi/2) = 0 $

$ sin(-pi/2) = -1 $

Thus, the coordinates are:

$ (0, -1) $

To find the position of $-pi/2$ on the unit circle:

1. Move $pi/2$ radians clockwise.

2. Convert the angle to coordinates:

$ (cos(-pi/2), sin(-pi/2)) $

Resulting in:

$ (0, -1) $

Start Using PopAi Today