Proof Inverse Sin: Complete Series Proof

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    Inverse Proof Sin
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SUMMARY

The discussion centers on finding a complete proof of the infinite series for arcsin, specifically through the Taylor series. A user seeks a method to derive arcsin using the unit circle, highlighting a practical application in tutoring trigonometry. The provided link to PlanetMath offers a resource for the Taylor series of arcsin, which is essential for understanding the mathematical foundation of this function. The inquiry emphasizes the relationship between trigonometric functions and their inverses, particularly in educational contexts.

PREREQUISITES
  • Understanding of Taylor series and their applications in calculus.
  • Familiarity with trigonometric functions, specifically sine and arcsine.
  • Knowledge of the unit circle and its significance in trigonometry.
  • Basic skills in mathematical proof techniques.
NEXT STEPS
  • Study the derivation of the Taylor series for arcsin using calculus.
  • Explore the geometric interpretation of arcsin on the unit circle.
  • Learn about the relationship between trigonometric functions and their inverses.
  • Investigate other infinite series representations for trigonometric functions.
USEFUL FOR

Students, educators, and mathematicians interested in trigonometry, particularly those looking to deepen their understanding of arcsin and its derivation through the unit circle and Taylor series.

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Can someone tell me where I can find a complete proof of the infinite series used to find the arcsin? thanks in advance.
 
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http://planetmath.org/encyclopedia/TaylorSeriesOfArcusSine.html
 
Last edited by a moderator:
nicksauce said:
http://planetmath.org/encyclopedia/TaylorSeriesOfArcusSine.html

Thank you for link. I apologize I should have been more specific with my question.

I actually wanted to see a proof or some method that specifically creates arcsin. I ask because I was tutoring a student one day in trig and was trying to get the angle of sin based on the output of the sin with that unknown angle. To make a long story short I realized I never needed the angle measure to begin with but I was curious to see if there's a way to get the angle of a trig function just based on using the unit circle. I guess that's my real question: is there a way to get arcsin just by using the unit circle?
 
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