# How do you find the trigonometric functions of any angle?

##### 1 Answer
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: $\theta = \frac{\pi}{6} = \frac{3.14}{6} = 0.523$ and:
$\sin \left(\frac{\pi}{6}\right) = \sin \left(0.523\right) = 0.523 - 0.024 + 3.26 \cdot {10}^{- 4} - \ldots = 0.499 \approx 0.5$

You can find the Taylor series for the other trigonometric functions such as:

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