QII reference angle
180°-Θ
A reference angle is the positive acute angle formed by the terminal side of an angle and the x-axis in the standard position. To find the reference angle, we should follow these steps:
1. Draw the angle in the standard position.
2. Identify the quadrant in which the angle lies.
3. Determine the distance between the terminal side of the angle and the nearest x-axis.
4. If the distance determined in step 3 is greater than 90 degrees, subtract it from 180 degrees to obtain the reference angle. If the distance is less than or equal to 90 degrees, the distance is equivalent to the reference angle.
For example, suppose we have an angle of 165 degrees. Here are the steps we follow to find its reference angle:
1. Draw the angle in the standard position as shown below.
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2. Identify the quadrant in which the angle lies. In this case, the angle lies in the second quadrant.
3. Determine the distance between the terminal side of the angle and the nearest x-axis. The distance between the terminal side and the x-axis is 15 degrees.
4. Since the distance is less than 90 degrees, the distance is equivalent to the reference angle. Therefore, the reference angle for the angle of 165 degrees is 15 degrees.
The reference angle is extremely useful when solving trigonometric functions, especially in finding the exact value of trigonometric functions of larger angles.
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