How to Find a Reference Number

••• pi image by Ewe Degiampietro from

Finding the reference number in your calculus equation can make the difference between passing your introductory calculus test and class, and having to retake the course. The reference number is identified as the shortest distance along the unit 360 degrees circle between the x-axis and the terminal or ending point of the circle angle. Finding the reference number requires you to understand circle angles and the radians of a circle in terms of pi.

    Familiarize yourself with circle angles. On a graphed plane with four quadrants, circle angles are split up into numerals with pi symbols. For example, 180 degree = pi while 360 degree = 2 pi.

    Figure out the terminal point of the equation. The terminal point is the x and y coordinates of your circle angle. Take the angle and check the circle angle wheel to figure out what your terminal point is.

    Calculate the reference number. The reference number equals pi – the terminal point. For example, if your terminal point = 5 pi / 6, your reference number = pi / 6. Pi would equal 6 pi / 6, and 6 – 5 = 1 or 1 pi / 6. Simplify 1 pi / 6 to pi / 6.


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