Reference Angle Calculator

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The reference angle calculator is used to calculate the reference angle of any of the angle given to us. Reference angle is positive acute angle formed by the x axis. Reference angle on the x-y plane is always between 0 to 90 degrees. It is the smallest angle that we can make from the terminal side of the angle. Trigonometric functions have the same value for the angle and for the reference angle.

 
Example 1: Find the reference angle of 170 degrees.

For a given angle, the reference angle is calculated by looking at the quadrant it is lying in and this angle lies in the second

quadrant

For the second quadrant the reference angle is equal to 180-x.

Reference angle = 180-x

Reference angle = 180-170 degrees


180-170 = 10 degrees

 Reference angle = 10 degrees

Hence the value of the reference angle is 10 degrees

 


Example 2: Calculate the reference angle of 210 degrees.

For a given angle, the reference angle is calculated by looking at the quadrant it is lying in and this angle lies in the third

quadrant

For the second quadrant the reference angle is equal to x-180.

Reference angle = x-180

Reference angle = 210-180 degrees

210-180 = 30 degrees

Reference angle = 30 degrees

Hence the value of the reference angle is 30 degrees

 

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