Mathematical Problems sidong cunt brick utego (32.1.) Show that the Madhava-Jyesthadeva formula given at the beginning of the chapter is equivalent to or, letting x = tan 6, 0 =(-1* tan24+18 2k + 1 k=0 arctan x= +24+1 2k + 1 (-1)₂ k=0
Mathematical Problems sidong cunt brick utego (32.1.) Show that the Madhava-Jyesthadeva formula given at the beginning of the chapter is equivalent to or, letting x = tan 6, 0 =(-1* tan24+18 2k + 1 k=0 arctan x= +24+1 2k + 1 (-1)₂ k=0
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Mathematical Problems
sidong cut back
(32.1.) Show that the Madhava-Jyesthadeva formula given at the beginning of the chapter
is equivalent to
or, letting x = tan 0,
0
=(-1) tan24+18
2k + 1
k=0
arctan x=
8
+2k+1
2k + 1
(-1);
k=0
DALE
![The product of the given Sine and the radius divided by the Cosine is the first result. From
the first,... etc., results obtain...a sequence of results by taking repeatedly the square of the
Sine as the multiplier and the square of the Cosine as the divisor. Divide... in order by the odd
numbers one, three, etc... From the sum of the odd terms, subtract the sum of the even terms.
[The result] becomes the arc. [Rajagopal, 1993, p. 98]
These instructions give in words an algorithm that we would write as the following
formula, remembering that the Sine and Cosine used in earlier times correspond to our
r sine and r cos 0, where r is the radius of the circle:
Madhava-
A sin³0
3r3 cos³ 0
re
Jyesthadeva
² sine
formula
r cos 0
The bulk of calculus was developed in Europe during the seventeenth century, and it is
on that development that the rest of this chapter is focused.
6 sine
+
5r5 cos
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7011b814-0888-4e7c-ad26-86019bf83fb9%2Fb2bfa02c-0122-4133-b10a-47d3259d1e35%2F233fw7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The product of the given Sine and the radius divided by the Cosine is the first result. From
the first,... etc., results obtain...a sequence of results by taking repeatedly the square of the
Sine as the multiplier and the square of the Cosine as the divisor. Divide... in order by the odd
numbers one, three, etc... From the sum of the odd terms, subtract the sum of the even terms.
[The result] becomes the arc. [Rajagopal, 1993, p. 98]
These instructions give in words an algorithm that we would write as the following
formula, remembering that the Sine and Cosine used in earlier times correspond to our
r sine and r cos 0, where r is the radius of the circle:
Madhava-
A sin³0
3r3 cos³ 0
re
Jyesthadeva
² sine
formula
r cos 0
The bulk of calculus was developed in Europe during the seventeenth century, and it is
on that development that the rest of this chapter is focused.
6 sine
+
5r5 cos
0
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