How do you find #sin(pi/12)# and #cos(pi/12)#?
I would use the expansion in series of the two functions, as
(have a look at the page: http://en.wikipedia.org/wiki/Taylor_series for more info)
Where a function (in a point) is given by an infinite sum of values.
We choose few values only, depending upon the accuracy we want (basically, decimal digits you want).
For your case (3 decimals only):
Now you can try to do the same by yourself with
hope it helps
Here is another way to solve this problem.
It's known that
Let's use a formula for a sine of a double angle:
Using this formula,
Substitute for simplicity:
Both are positive (since an angle
We have a system of two equations with two unknowns:
Adding the second equation to the first, we get
Subtracting the second equation from the first, we get
So, we have a very simple system of two equations with two unknowns:
Adding and subtracting this equations, we find solutions:
Use the cosine and sine half angle formulas:
First, let's solve for
We will take the positive root since the angle is
The cosine method is almost identical. The positive root will again be taken because cosine is also positive in the first quadrant.