How do you find the trigonometric functions of any angle?

1 Answer
Gió
Dec 22, 2014

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)

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