A reference angle is the smallest possible angle made by the terminal side of a given angle with the x-axis/7%3A_Trigonometry/7.02%3A_Reference_Angles). It is always an acute angle, except when it is exactly 90 degrees. The reference angle is always positive, irrespective of which side of the axis it is falling. The reference angle is important in finding the values of trigonometric ratios and in representing trigonometric functions on graphs. To draw the reference angle for an angle, identify its terminal side and see by what angle the terminal side is close to the x-axis. If the angle is in radians, then we use the same rules as for degrees by replacing 180° with π and 360° with 2π.

To find the reference angle of an angle, we can use the following rules:

• If the angle is in quadrant I, the reference angle is equal to the angle in quadrant I.
• If the angle is in quadrant II, the reference angle is 180 minus the angle in quadrant II.
• If the angle is in quadrant III, the reference angle is the angle in quadrant III minus 180.
• If the angle is in quadrant IV, the reference angle is 360 minus the angle in quadrant IV.

Reference angles can be used to find the sine and cosine of the original angle. The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle. The signs of the sine and cosine are determined from the x- and y-values in the quadrant of the original angle.