Integration involving inverse trigonometric functions (HSC SSCE Mathematics Extension 1): Flashcards
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What is the definition of sin^-1(x)?
What is the definition of sin^-1(x)?
y = sin^-1(x) finds angle when sine is x.
What is the range of the inverse sine function?
What is the range of the inverse sine function?
Range is [-π/2, π/2].
What is the derivative of cos^-1(x)?
What is the derivative of cos^-1(x)?
d/dx[cos^-1(x)] = -1/√(1-x²).
What is the domain of tan^-1(x)?
What is the domain of tan^-1(x)?
Domain is all real x.
What is the integral of 1/√(a²-x²)?
What is the integral of 1/√(a²-x²)?
∫1/√(a²-x²) dx = sin^-1(x/a) + C.
What is the derivative of sin^-1(x)?
What is the derivative of sin^-1(x)?
d/dx[sin^-1(x)] = 1/√(1-x²).
What is the integral of 1/(a²+x²)?
What is the integral of 1/(a²+x²)?
∫1/(a²+x²) dx = (1/a)tan^-1(x/a) + C.
What is the range of cos^-1(x)?
What is the range of cos^-1(x)?
Range is [0, π].
How do you calculate the angle of elevation?
How do you calculate the angle of elevation?
Use tan^-1(opposite/adjacent) for elevation.
What is the integral of 1/(x²-a²) dx?
What is the integral of 1/(x²-a²) dx?
∫1/(x²-a²) dx = (1/2a)ln| (x-a)/(x+a) | + C.