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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