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Trigonometric Functions of Any Angle

Key Questions

  • Well, the reference angle is the angle [the one which is the smallest] between the #x#-axis and the terminal side.

    Happy to Help:}

  • 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.

  • 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)

Questions