## Signs of Angles in Standard Position

### In mathematics, when we refer to the “standard position” of an angle, we mean that the vertex of the angle is located at the origin (0,0) on a coordinate plane, and the initial side of the angle is along the positive x-axis

In mathematics, when we refer to the “standard position” of an angle, we mean that the vertex of the angle is located at the origin (0,0) on a coordinate plane, and the initial side of the angle is along the positive x-axis. Based on this standard position, the signs of the angles can be determined as follows:

1. Positive Angle: A positive angle is formed when the terminal side of the angle rotates counterclockwise from the positive x-axis. The measure of a positive angle is always greater than 0 and less than 360 degrees or 2π radians.

2. Negative Angle: A negative angle is formed when the terminal side of the angle rotates clockwise from the positive x-axis. The measure of a negative angle is always less than 0 and greater than -360 degrees or -2π radians. Negative angles are also sometimes represented by reversing the sign of the angle measure.

Here are a few examples to illustrate the signs of angles in standard position:

– If an angle is formed by rotating counterclockwise from the positive x-axis, it is a positive angle. For example, if the terminal side of an angle goes through the first quadrant, it is positive.

– If an angle is formed by rotating clockwise from the positive x-axis, it is a negative angle. For example, if the terminal side of an angle goes through the fourth quadrant, it is negative.

– A positive angle can be represented as +θ or simply θ, where θ is the measure of the angle in degrees or radians.

– A negative angle can be represented as -θ or θ’ (θ prime), where θ is the measure of the angle in degrees or radians.

It’s important to note that positive and negative angles are simply different rotations in opposite directions from the positive x-axis. The signs of the angles are used to indicate their direction of rotation.

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