![]() ![]() ![]() There are four possible cases:Ĭase 1: (For Angles between 0° to 90°) – When the terminal side is on the first quadrant, the reference angle is the same as the given angle. We can find reference angles depending on which quadrant the terminal side of the angle is located in either degrees or radians. ‘C’ for cosine: In the fourth quadrant, only the cosine function has positive value Formulas How to Find a Reference Angle ‘T’ for tangent: In the third quadrant, tangent and cotangent have positive values ‘S’ for sine: In the second quadrant, only the sine function has positive value ‘A’ for all: In the first quadrant, all functions have positive value The only thing that varies is the sign.įollow the mnemonic rule: ‘ Add Sugar To Coffee’ or ‘ All Students Take Calculus’ to remember when these functions have positive values. Normally, the four trigonometric functions: sine, cosine, tangent, and cotangent give the same value for an angle and its reference angle. The numbering starts from the upper right one, the first quadrant, where both coordinates are positive as we continue to move in the anticlockwise direction. The two axes, x, and y divide the plane into four quadrants, named I, II, III, and IV. Reference Angles and Trigonometric Functions Looking at the picture above, every angle is measured from the positive part of the x-axis to its terminal side by traveling in a counterclockwise direction. A reference angle always uses an x-axis as its frame of reference. ![]() Their value is always between 0 and 90° when measured in degrees or 0 and π/2 when measured in radians. The reference angle is used for simplifying the calculations related to trigonometric functions with different angles. ![]()
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