Notice that the terminal sides of the angles measuring 30 degrees and 210 degrees 60 degrees and 240 degrees and so on form straight lines. As you can see from the figure above the reference angle is always less than or equal to 90 even for very large angles.

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The positive y axis is 90 or radians.

Reference angle for negative angles. Drag the point around the origin several times. The sine of 52 is the ratio of the opposite side ac to the hypotenuse ab. In a right triangle the angle can only lie in the range 0 90.

Identify your initial angle. Find out the quadrant your angle is in 0 to 90. The reference angle is always the smallest angle that you can make from the terminal side of an angle ie where the angle ends.

The reference angle is the positive acute angle that can represent an angle of any measure. You get the positive angle. The negative x axis is 180 or π radians.

This fact is to be expected because the angles are 180 degrees apart and a straight angle measures 180 degrees. And the negative y axis is 270 or radians. When finding reference angles it can be helpful to keep in mind that the positive x axis is 0 and 360 or 0 radians and 2π radians.

Note how the reference angle always remain less than or equal to 90 even for large angles. For large angles the same idea applies. Note that the angle b is 52.

For this example we ll use 440 2. Determine the quadrant in which the terminal side lies. B 249 is in quadrant iii 180 249 270 the reference angle is 249 180 69 c 328 is in quadrant iii 270 328 360 the reference angle is 360 328 32 what are reference angles are and how to find them and then how to use them to determine.

How to find reference angle in radians. A 340 degree angle is equivalent to a 20 degree angle. 0 to π 2 first quadrant so reference angle angle π 2 to π second quadrant so reference angle π angle π to 3π 2 third quadrant so reference angle angle π 3π 2 to 2π fourth quadrant so reference angle 2π angle.

Basically any angle on the x y plane has a reference angle which is always between 0 and 90 degrees. Angles in the first quadrant are their own reference angle so. Finding a reference angle in degrees is straightforward if you follow the correct steps.

Do the operation indicated for that quadrant. In the figure above click on reset. It is always 90.

The angle is larger than a full angle of 360 so you need to subtract the total angle until it s small. Is defined as the ratio of the opposite side to the hypotenuse. To find the reference angle for 340 degrees.

440 360 80 3.