reference angle
used to find the trig values of any angle (theta). It is an acute angle formed by the terminal side and the x-axis.
The reference angle is the acute angle between the terminal side of an angle in standard position (meaning the vertex is at the origin and one side lies along the positive x-axis) and the x-axis. Essentially, it is the smallest angle formed between the terminal side and the x-axis.
To find the reference angle of an angle, follow these steps:
1. Determine the quadrant in which the angle lies.
2. If the angle is in the second, third, or fourth quadrant, find the distance between the angle’s terminal side and the nearest x-axis line (positive or negative). This distance will be equal to the reference angle.
3. If the angle is in the first quadrant, the reference angle is simply the angle itself.
Note that when finding the reference angle for an angle in the second or third quadrant, we take the distance to the x-axis line in the positive direction, while for an angle in the fourth quadrant, we take the distance to the x-axis line in the negative direction.
Knowing the reference angle can be useful in simplifying trigonometric expressions and calculations, especially when dealing with angles greater than 90 degrees.
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