“The smallest measure of the angle this is shaped with the aid of becoming a member of the tremendous x-axis and the terminal line is referred to as the reference angle”
There get up two cases which are as follows:
below are the formulation to locate reference angles in stages:
First Quadrant: \(0^\text{o} - 90^\text{o}\) \(Reference Angle = Angle\)
Second Quadrant: \(90^\text{o} - 180^\text{o}\) \(Reference Angle = 180^\text{o} - Angle\)
Third Quadrant: \(180^\text{o} - 270^\text{o}\) \(Reference Angle= Angle - 180^\text{o}\)
Fourth Quadrant: \(270^\text{o} - 360^\text{o}\) \(Reference Angle = 360^\text{o} - Angle\)
Reference angle In Radians:
First Quadrant: \(0 - \frac{\pi}{2}\) \(Reference Angle = Angle\)
Second Quadrant: \(\frac{\pi}{2} - \pi\) \(Reference Angle= \pi - Angle\)
Third Quadrant: \(\pi - \frac{3 \pi}{2}\) \(Reference Angle= Angle - \pi\)
Fourth Quadrant: \(\frac{3 \pi}{2} - 2 \pi\) \(Reference Angle= 2 \pi - Angle\)
All of the above-stated reference attitude formulation are summarized inside the following pictorial illustration:
in this section, we are able to cognizance on clarifying your concept more exactly by way of resolving more than one example.
a way to discover the reference attitude in radians corresponding to \(60^\text{o}\)?
Solution:
First, we will convert the given angle in radians:
\(Angle In Radians= \text{Angle In Degrees} * \frac{\pi}{180}\)
\(Angle In Radians = (60^\text{o}) * \frac{3.14}{180}\)
\(Angle In Radians = 1.047 rad \)
As the given angle lies in the first quadrant, the reference angle is the same as the given angle:
\(Reference Angle = 1.047 rad\)
employ this reference angle finder to find a reference angle in more than one clicks. aggravating approximately the use of this unfastened calculator? let us go!
Input:
Output: The loose fashionable role calculator calculates:
Reference angles make it possible in order to determine the trigonometric angles that lie outdoor the first quadrant. also, you can use those precise angles to find the coordinates of the angles.
