Question
Find the Taylor polynomialof order 5 appoximation to sin(1.5)
Answers
Reiny
sinx = x - x^3/3! + x^5/5! - ...
sin 1.5 = 1.5 - (1.5)^3/6 + (1.5)^5/120
= 1.5 - .5625 + .06328 -
= 1.00078
my calculator said
tan 1.5 = .997495
so clearly 3 terms are not sufficient for good accuracy, (sine can't have a value > 1)
Taking one more term, -(1.5)^7/7! would bring it to .9974
sin 1.5 = 1.5 - (1.5)^3/6 + (1.5)^5/120
= 1.5 - .5625 + .06328 -
= 1.00078
my calculator said
tan 1.5 = .997495
so clearly 3 terms are not sufficient for good accuracy, (sine can't have a value > 1)
Taking one more term, -(1.5)^7/7! would bring it to .9974