1. Show that for all z € [0, π/4], the estimates 1³ 15 3! 5! sin (r) r - + and cos(x) = 1 have error < 0.0005 and < 0.00005, respectively. (In the olden days, via trigonometric identities and reference angles, this allowed people to compute sin and cos of any number with error < 0.001, by just knowing how close it is to the nearest. quarter of . E.g. sin(17) = = -cos (2-17) cos(0.2787) 1-0.27872 +0.2787 -0.961.) 41
1. Show that for all z € [0, π/4], the estimates 1³ 15 3! 5! sin (r) r - + and cos(x) = 1 have error < 0.0005 and < 0.00005, respectively. (In the olden days, via trigonometric identities and reference angles, this allowed people to compute sin and cos of any number with error < 0.001, by just knowing how close it is to the nearest. quarter of . E.g. sin(17) = = -cos (2-17) cos(0.2787) 1-0.27872 +0.2787 -0.961.) 41
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please give me answer very fast in 5 min sub
![1.
Show that for all ze [0, π/4], the estimates
x3
sin(x) x- +
3! 5!
and
cos(x) ≈ 1
-
have error< 0.0005 and < 0.00005, respectively.
(In the olden days, via trigonometric identities and reference angles, this allowed people to
compute sin and cos of any number with error < 0.001, by just knowing how close it is to the nearest
quarter of T. E.g. sin(17) = (217)-cos(0.2787) 1-0.27872
-0.961.)
= COS
0.27874
41](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b7051cb-c171-4435-8abe-129babaf0b12%2F49e2a4c9-7242-4556-b2c6-cff17d9f787b%2F1euzsxw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
Show that for all ze [0, π/4], the estimates
x3
sin(x) x- +
3! 5!
and
cos(x) ≈ 1
-
have error< 0.0005 and < 0.00005, respectively.
(In the olden days, via trigonometric identities and reference angles, this allowed people to
compute sin and cos of any number with error < 0.001, by just knowing how close it is to the nearest
quarter of T. E.g. sin(17) = (217)-cos(0.2787) 1-0.27872
-0.961.)
= COS
0.27874
41
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