On Inverse Trigonometric Functions

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SUMMARY

This discussion focuses on solving three specific problems related to inverse trigonometric functions. The first problem involves solving the equation arcsin(6x - π) = 1/8, which requires taking the sine of both sides. The second problem asks for the equation of the tangent line to the graph of y = arcsin(6x) at the point (1/(6√2), π/4), necessitating differentiation of the function. The third problem involves finding the indefinite integral of 1/√(81 - 100x²), which can be approached using trigonometric substitutions.

PREREQUISITES
  • Understanding of inverse trigonometric functions
  • Proficiency in differentiation techniques
  • Knowledge of trigonometric identities and substitutions
  • Familiarity with solving equations involving arcsin
NEXT STEPS
  • Study the properties and applications of inverse trigonometric functions
  • Learn differentiation techniques for composite functions
  • Explore trigonometric substitution methods for integrals
  • Practice solving equations involving arcsin and other inverse functions
USEFUL FOR

Students, educators, and anyone studying calculus or advanced mathematics, particularly those focusing on inverse trigonometric functions and their applications.

Moonflower
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Hi, can you help me solve these three questions? Please show each step. Thanks.

1. solve for x: arcsin(6x-pi)=1/8
2. Find an equation of the tangent line to the graph of y = arcsin (6x) at the point ((1/(6sqrt2),(pi/4))
3. Find the indefinite integral of 1/sqrt(81-100x^2)
 
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1. Start by taking the sine of both sides.
2. Its a well-known problem, start by differentiate the function. You are supposed to know how to complete it.
3. Note that 100x^2=(10x)^2 , think about the trigonometric substitutions.



S
 

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