Proof Inverse Sin: Complete Series Proof

In summary, the conversation discusses the search for a complete proof of the infinite series used to find the arcsin. The person initially asks for a link to the Taylor series of arcsin, but later clarifies that they are looking for a method to specifically create arcsin using the unit circle.
  • #1
bfd
45
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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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  • #2
http://planetmath.org/encyclopedia/TaylorSeriesOfArcusSine.html
 
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  • #3
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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Related to Proof Inverse Sin: Complete Series Proof

1. What is the concept of inverse sin in the "Proof Inverse Sin: Complete Series Proof"?

The concept of inverse sin in this series is the mathematical operation that allows you to find the angle in a right triangle given the ratio of the opposite side and the hypotenuse.

2. How is inverse sin different from regular sin?

Inverse sin is the opposite operation of sin. While sin takes an angle as input and gives the ratio of the opposite side and the hypotenuse, inverse sin takes the ratio as input and gives the angle as output.

3. What is the importance of inverse sin in mathematics?

Inverse sin is an essential concept in trigonometry and is used to solve problems related to angles and sides in right triangles. It also has applications in physics, engineering, and other fields.

4. How is inverse sin calculated?

The inverse sin of a ratio is calculated using the inverse sine function on a calculator or by using the formula sin-1(opposite/hypotenuse). This gives the angle in radians, which can be converted to degrees if needed.

5. What are some real-life examples of using inverse sin?

Inverse sin can be used in various real-life situations, such as measuring the height of a tree or building using the angle of elevation, determining the angle of a ramp for wheelchair accessibility, and calculating the trajectory of a projectile in physics.

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