# Related Angles

# Related Angles

## What are Related Angles in Trigonometry?

**Related angles**refer to angles that have the same trigonometric functions (sin, cos, tan) but are in different locations in a standard coordinate plane.- For any angle θ, the related angle is the measure of the angle when it’s reduced to fall within the range of 0 to 360 degrees.
- This concept helps in expanding the scope of trigonometric functions beyond the basic 0-90 degrees.

## Positive and Negative Angles

**Positive angles**are measured counterclockwise from the initial side (usually the x-axis), whereas**negative angles**are measured clockwise.- This concept is important because the trigonometric value of an angle is the same, whether it is measured positively or negatively.

## Quadrantal Angles

- Quadrants divide the plane into four sections. These are known as
**quadrantal angles**, which are multiples of 90 degrees. - Quadrantal angles are useful when conducting more detailed analyses of trigonometric functions.
- It’s crucial to understand that sine, cosine, and tangent functions take on different signs depending on which quadrant the terminal side of the angle lies in.

## Co-Related Angles

**Co-related angles**are angles that add up to either 90 or 180 degrees. They help to establish the relationships that exist between the measures of the angles of a right triangle.- These angles can simplify complex problems by invoking the symmetry and periodicity of the sine, cosine, and tangent functions.

## Calculating Trigonometric Values of Related Angles

- The
**trigonometric values of related angles**can be found using reference angles and the signs of the trigonometric functions in each quadrant. - These methods help in generalising the trigonometric values across all angles, making it easier to solve more complex trigonometry problems.

Remember, proper grasp of related angles concept, the trigonometric functions associated with them and the application of these concepts are absolutely crucial to solving trigonometric problems involving angles outside the standard 0-90 degree range.