How do I evaluate cos(pi/10) without using a calculator?
1 Answer
Explanation:
For this purpose we can use the Maclaurin series or the Taylor series. Since
The Maclaurin series is given by
Finding the coefficients
And
We can stop when the term of the series, different of zero, is inferior to the precision required.
Setting
Estimating (with
x=0.3 ) the function in 2 terms we have
f(x=0.3)=1-0.09/2=1-0.045=0.955
Estimating (withx=0.3 ) the function in 3 terms we have
f(x=0.3)=1-0.09/2+0.008/24=1-0.045+0.0003=0.9553
As we can see there's no need to work with this function with more than 2 terms since the desconsideration of the terms after the second one doesn't compromise the result with the intended accuracy.
So, with 3 significant digits, a good approximation of the function is
Calculating
>
Using
f(x=0.314)=1-0.0986/2=1-0.0493=0.9507
In 3 significant digits:
f(x=0.314)=0.951