How do you find the exact value of $12(sin150)(cos150)$ ?

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Answer 1 · 2016-11-27T10:27:16

$sin 150 = sin((5pi)/6) = 1/2$
$cos 150 = cos((5pi)/6) = -(sqrt(3))/2$

$12*1/2*(-(sqrt(3))/2)=-3sqrt(3)$

You have to know the three basic "magic" numbers of sin and cos goniometric functions. They are: $1/2$ , $sqrt(2)/2$ , $sqrt(3)/2$ .

Also calculating with radians may help you.
You know that $1pi$ rad equals 180°.

Here is the unit circle, where you can find all sin and cos values for the basic angles.

![https://www.mathsisfun.com/geometry/http://unit-circle.html](https://useruploads.socratic.org/ftWVIcuZT3iSzqsVP9cx_circle-unit-radians.gif)
I used an image from this page:
https://www.mathsisfun.com [online]. [cit. 2016-11-27]. Available from: https://www.mathsisfun.com/geometry/unit-circle.html

How do you find the exact value of 12(sin150)(cos150)12(sin150)(cos150)?