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Inverse Trigonometric Functions

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Questions and Answers

What is the most common notation for inverse trigonometric functions?

arcsin(x), arccos(x), arctan(x) (correct)

asin, acos, atan

sin−1(x), cos−1(x), tan−1(x)

sin(x)^-1, cos(x)^-1, tan(x)^-1

What are the inverse functions of the sine, cosine, and tangent functions called?

Sine^-1, Cosine^-1, Tangent^-1

Arcsin, Arccos, Arctan

Arcsine, Arccosine, Arctangent (correct)

Cosecant, Secant, Cotangent

What is the main purpose of inverse trigonometric functions?

Obtaining an angle from a trigonometric ratio (correct)

Finding the derivative of a trigonometric function

Solving trigonometric equations

Calculating the area of a triangle

In what fields are inverse trigonometric functions widely used?

Engineering, navigation, physics, and geometry Signup and view all the answers

What geometric relationship gives rise to the 'arc-' prefix in the notation of inverse trigonometric functions?

$r\theta$ corresponds to an arc length Signup and view all the answers

What is the condition for the existence of the inverse of a function f?

f must be bijective Signup and view all the answers

How is the inverse of a function f denoted?

$f^{-1}$ Signup and view all the answers

What is the explicit description of the inverse function $f^{-1} : Y \to X$?

$f^{-1}(y) = x$ such that $f(x) = y$ Signup and view all the answers

When is a function f invertible?

If there exists a function g such that $g(f(x)) = x$ for all $x \in X$ and $f(g(y)) = y$ for all $y \in Y$ Signup and view all the answers

What is the notation for the inverse function of a real-valued function given by $f(x) = 5x - 7$?

$f^{-1}(y) = \frac{y + 7}{5}$ Signup and view all the answers