# Reflecting on Reference Angles in Trigonometry

## How can we determine the reference angles for different given angles in trigonometry?

Let's explore how reference angles are calculated for various angles in trigonometry.

## Calculating Reference Angles

In trigonometry, reference angles are important in determining the relationship between an angle and the x-axis. By finding the reference angle, we can simplify trigonometric calculations and better understand the position of the angle in a specific quadrant.

Let's calculate the reference angles for the following angles:

- Angle θ = 300 degrees
- Angle θ = 225 degrees
- Angle θ = 480 degrees
- Angle θ = -210 degrees

## 1. Calculating the Reference Angle for 300 Degrees

For an angle of 300 degrees:

300 degrees is in the 4th quadrant.

Therefore, the reference angle is:

α = 360 - θ

α = 360 - 300

α = 60 degrees

Hence, the reference angle of 300 degrees is 60 degrees.

## 2. Calculating the Reference Angle for 225 Degrees

For an angle of 225 degrees:

225 degrees is in the 3rd quadrant.

Therefore, the reference angle is:

α = θ - 180

α = 225 - 180

α = 45 degrees

Hence, the reference angle of 225 degrees is 45 degrees.

## 3. Calculating the Reference Angle for 480 Degrees

For an angle of 480 degrees:

480 degrees is in the 2nd quadrant (i.e. 480 - 360 = 120).

Therefore, the reference angle is:

α = 180 - θ

α = 180 - 120

α = 60 degrees

Hence, the reference angle of 480 degrees is 60 degrees.

## 4. Calculating the Reference Angle for -210 Degrees

For an angle of -210 degrees:

-210 degrees is in the 3rd quadrant (i.e. 360 - 210 = 150).

Therefore, the reference angle is:

α = 180 - θ

α = 180 - 150

α = 30 degrees

Hence, the reference angle of -210 degrees is 30 degrees.