AP PreCalculus Flashcards: Inverse Trigonometric Functions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What is the restricted domain of the cosine function used to define the arccosine function?
To define the arccosine function, the domain of the cosine function is restricted to the closed interval $[0, \\pi]$.
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What is the restricted domain of the cosine function used to define the arccosine function?
To define the arccosine function, the domain of the cosine function is restricted to the closed interval $[0, \\pi]$.
What is the restricted domain of the sine function used to define the arcsine function?
To define the arcsine function, the domain of the sine function is restricted to the closed interval $[-\\frac{\\pi}{2}, \\frac{\\pi}{2}]$.
In the expression y = arccos(x), what does the input value 'x' represent?
The input 'x' is a value in the range of the corresponding trigonometric function, which for cosine is a value between -1 and 1.
What are the alternative names for the inverse sine, inverse cosine, and inverse tangent functions?
The inverse trigonometric functions are also called arcsine, arccosine, and arctangent.
What is the range of the arccosine function?
The range of arccosine is the restricted domain of the cosine function, which is $[0, \\pi]$.
Why must the domains of trigonometric functions be restricted to define their inverses?
Because the corresponding trigonometric functions are periodic, their domains must be restricted to make them one-to-one and thus invertible.
What is the range of the arctangent function?
The range of arctangent is the restricted domain of the tangent function, which is $(-\\frac{\\pi}{2}, \\frac{\\pi}{2})$.
What is the range of the arcsine function?
The range of arcsine is the restricted domain of the sine function, which is $[-\\frac{\\pi}{2}, \\frac{\\pi}{2}]$.
In the expression y = arcsin(x), what does the output value 'y' typically represent?
The output value of an inverse trigonometric function, such as 'y' in y = arcsin(x), is interpreted as an angle measure.
What is the restricted domain of the tangent function used to define the arctangent function?
To define the arctangent function, the domain of the tangent function is restricted to the open interval $(-\\frac{\\pi}{2}, \\frac{\\pi}{2})$.