Q:Considering the exact value of sin(pi/six), let x=pi/6 and evaluate x, x-x^3/3
ID: 2871878 • Letter: Q
Question
Q:Considering the exact value of sin(pi/six), let x=pi/6 and evaluate x, x-x^3/3!, x-x^3/3!+x^5/5!, x-x^3/3!+x^5/5!-x^7/7!+, and so on. Which is the first expression to give you 0.5?
Answer: pi/6 - (pi/6)^3/3! + (pi/6)^5/5! = 0.50 .The third expression of the series will give the closest answer to 0.50 first.
Q: Let x= pi/4 and evaluate 1-x2/2!, 1-x2/2 + x4/4!, 1-x2/2 + x4/4! - x6/6!, and so on. Which expression is the first to agree with the value of cos(pi/4) ?
Answer: 1 - (9pi/4)^2/2! + (9pi/4)^4/4! = 0.7071 . The third expression of the series gives the closest answer first.
FAQ: There are no finite algebraic formulas that will produce the values of the functions of sin(x) and cos(x). They are transcendental. The sine and cosine functions can be evaluated using infinite algebraic formulas called infinite series.
-The idea of these exercises were to give one an idea of what a calculator does when it determines a sine or cosine.
-Now the big question is what can you conjecture about the size of x and the number of terms needed to give an accurate value for sin (x) and cos (x)? The answer is not Three (as I've wasted almost four questions previous to this one).
MAIN QUESTION!!!!: HOW IS THE SIZE OF X AND THE NUMBER OF TERMS RELATED, AND WHY????
Explanation / Answer
We can take any number of terms and size of x depends valueof function
after some decimal points value being same
For example :
1st term : 0.1203251
2nd Term : 0.134568
3rd term : 0.168493
4th Term : 0.1925634
5th Term : 0.206849
6th Term : 0.206850
7th Term : 0.206851
so we can see 5th, 6th and 7th term value after 5th decimal value change , upto 5th decimal it same
So we can take upto 6th or 7th term.
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