5. The arcsin function is the inverse of sin on [-1, 1]. (a) Differentiate (implicitly) sin(y) = x to show that d arcsin(x) = (1 – x²)-1/2. d.x (To review this, see Section 5 of the Maths 130 coursebook) (b) Derive a formula for the Maclaurin series of arcsin(x). (Hint: use (a) and the series in the previous question.) (c) Use part (b) and the fact that sin() = ; to derive a series that computes T. (d) Compute the sum of the first 4 terms of the series in (c). How close to T is your answer?
5. The arcsin function is the inverse of sin on [-1, 1]. (a) Differentiate (implicitly) sin(y) = x to show that d arcsin(x) = (1 – x²)-1/2. d.x (To review this, see Section 5 of the Maths 130 coursebook) (b) Derive a formula for the Maclaurin series of arcsin(x). (Hint: use (a) and the series in the previous question.) (c) Use part (b) and the fact that sin() = ; to derive a series that computes T. (d) Compute the sum of the first 4 terms of the series in (c). How close to T is your answer?
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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![5. The arcsin function is the inverse of sin on [-1, 1].
(a) Differentiate (implicitly) sin(y) = x to show that
d
arcsin(x) = (1 – x²)-1/2.
d.x
(To review this, see Section 5 of the Maths 130 coursebook)
(b) Derive a formula for the Maclaurin series of arcsin(x).
(Hint: use (a) and the series in the previous question.)
(c) Use part (b) and the fact that sin() = ; to derive a series that computes T.
(d) Compute the sum of the first 4 terms of the series in (c). How close to T is your answer?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab68ef6f-9760-4c1f-88a8-6e5ceb2168b2%2Fddc48ed9-0c60-4420-86e2-5af1e2835512%2F6lunhy09_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. The arcsin function is the inverse of sin on [-1, 1].
(a) Differentiate (implicitly) sin(y) = x to show that
d
arcsin(x) = (1 – x²)-1/2.
d.x
(To review this, see Section 5 of the Maths 130 coursebook)
(b) Derive a formula for the Maclaurin series of arcsin(x).
(Hint: use (a) and the series in the previous question.)
(c) Use part (b) and the fact that sin() = ; to derive a series that computes T.
(d) Compute the sum of the first 4 terms of the series in (c). How close to T is your answer?
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