Trig Inverse Integrals

Front

What is the definition of the inverse trigonometric function arcsin(x)?

Back

The inverse trigonometric function arcsin(x) is defined as the angle θ such that sin(θ) = x, where -1 ≤ x ≤ 1 and -π/2 ≤ θ ≤ π/2.

Front

What is the derivative of the inverse trigonometric function arcsin(x)?

Back

The derivative of arcsin(x) is 1/√(1 - x²), for -1 < x < 1.

Front

What is the definition of the inverse trigonometric function arccos(x)?

Back

The inverse trigonometric function arccos(x) is defined as the angle θ such that cos(θ) = x, where -1 ≤ x ≤ 1 and 0 ≤ θ ≤ π.

Front

What is the derivative of the inverse trigonometric function arccos(x)?

Back

The derivative of arccos(x) is -1/√(1 - x²), for -1 < x < 1.

Front

What is the definition of the inverse trigonometric function arctan(x)?

Back

The inverse trigonometric function arctan(x) is defined as the angle θ such that tan(θ) = x, where -∞ < x < ∞ and -π/2 < θ < π/2.

Front

What is the derivative of the inverse trigonometric function arctan(x)?

Back

The derivative of arctan(x) is 1/(1 + x²), for all x.

Front

What is the Second Fundamental Theorem of Calculus?

Back

The Second Fundamental Theorem of Calculus states that if F is an antiderivative of f on an interval [a, b], then ∫[a to b] f(x) dx = F(b) - F(a).

Front

How do you evaluate the integral of an inverse trigonometric function?

Back

To evaluate the integral of an inverse trigonometric function, you can use integration techniques such as substitution or integration by parts, depending on the specific function.

Front

What is the relationship between inverse trigonometric functions and right triangles?

Back

Inverse trigonometric functions can be interpreted in terms of right triangles, where the angle corresponds to the ratio of the lengths of the sides.

Front

What is the range of the arcsin function?

Back

The range of the arcsin function is [-π/2, π/2].