6. We can evaluate π by use of the equation 0.5m-tan-¹(1/2)+tan-¹(1/3). Meaning of this equation is: angle of 0.5π(in radians) is a sum of an angle corresponding to tan of value (1/2) (in radians) and angle corresponding to tan of value (1/3), in radians. The first three terms of the inverse tangent function are: tan-¹x=x- (1/3)x³+(1/5)x5. Use these three terms to expand tan-¹(1/2) and tan-¹(1/3) and approximate the value of 0.5π using the equation given above. Show your complete calculations. Compare your result with value of 0.5TT.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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6.
We can evaluate TT by use of the equation 0.5π-tan-¹(1/2)+tan ¹(1/3). Meaning
of this equation is: angle of 0.5m(in radians) is a sum of an angle corresponding to tan
of value (1/2) (in radians) and angle corresponding to tan of value (1/3), in
radians. The first three terms of the inverse tangent function are: tan-¹x=x-
(1/3)x³+(1/5)x5. Use these three terms to expand tan-1(1/2) and tan-¹(1/3) and
approximate the value of 0.5π using the equation given above. Show your complete
calculations. Compare your result with value of 0.5TT.
Transcribed Image Text:6. We can evaluate TT by use of the equation 0.5π-tan-¹(1/2)+tan ¹(1/3). Meaning of this equation is: angle of 0.5m(in radians) is a sum of an angle corresponding to tan of value (1/2) (in radians) and angle corresponding to tan of value (1/3), in radians. The first three terms of the inverse tangent function are: tan-¹x=x- (1/3)x³+(1/5)x5. Use these three terms to expand tan-1(1/2) and tan-¹(1/3) and approximate the value of 0.5π using the equation given above. Show your complete calculations. Compare your result with value of 0.5TT.
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