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Trigonometric Functions of Any Angle

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Math Analysis - Unit Circle - How to create the Unit Circle from scratch

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1 of 2 videos by AJ Speller

Key Questions

  • Well, I guess you could use a special representation of the function through a sum of terms, also known as Taylor Series.
    It is, basically, what happens in your pocket calculator when you evaluate, for example, #sin(30°)#.
    Your calculator does this:
    #sin(theta)=theta-theta^3/(3!)+theta^5/(5!)-...#
    where #theta# must be in RADIANS.
    In theory you should add infinite terms but, depending upon the accuracy required, you can normally stop at three terms.
    In our case we have: #theta=pi/6=3.14/6=0.523# and:
    #sin(pi/6)=sin(0.523)=0.523-0.024+3.26*10^(-4)-...=0.499approx0.5#

    You can find the Taylor series for the other trigonometric functions such as:
    enter image source here
    (Picture source: www.efunda.com)

  • Answer:

    As below:

    Explanation:

    Ordered pairs on an unit circle

    enter image source here

    Exact values of the ordered pairs of the unit circle is represented in pictorial form above in degrees and radians.

    Hope this helps.

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