Inverse Tangent Quiz: Inverse Tangent Fundamentals

  • 11th Grade
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| Attempts: 12 | Questions: 20 | Updated: Dec 17, 2025
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1) Which of the following are true about the inverse tangent function?

Explanation

arctan(1) = π/4 and arctan(−√3/2) = −π/3 are correct. arctan is not periodic, and it maps all real numbers to [−π/2, π/2], not [−π/4, π/4].

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About This Quiz
Inverse Tangent Quiz: Inverse Tangent Fundamentals - Quiz

What sets inverse tangent apart from other inverse trig functions? In this quiz, you’ll explore arctangent’s restricted range, analyze how it maps slopes to angles, and interpret its graph with clarity. You’ll evaluate expressions, recognize common outputs, and connect arctan behavior to real-world situations involving direction or orientation. Through practice... see moreproblems, you’ll develop strong intuition for how inverse tangent operates and learn to use it confidently when solving trigonometric equations or modeling applications.
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2) For θ = arctan(x), the equation tan(θ) = x holds for all real values of x.

Explanation

By the definition of the inverse tangent, tan(arctan(x)) = x for all real x.

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3) Arctan(−√3) = ____.

Explanation

tan(−π/3) = −√3, and since −π/3 lies in the principal range (−π/2, π/2), the correct value of the inverse tangent is −π/3.

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4) For y = arctan(x), the domain of this function is ____.

Explanation

The domain of arctan(x) is all real numbers, since the tangent function is defined for all real x.

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5) The function y = arctan(x) is increasing on its entire domain.

Explanation

arctan(x) is strictly increasing on its entire domain, which is all real numbers.

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6) Select all correct definitions of arctan(x).

Explanation

arctan is the inverse of tan, with range (−π/2, π/2), mapping negative x to negative values.

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7) Select all true statements for y = arctan(x).

Explanation

The domain of arctan(x) is all real numbers. The range is [−π/2, π/2]. Asymptotes occur at y = ±π/2.

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8) Arctan(1) = ____.

Explanation

tan(π/4) = 1, so arctan(1) = π/4.

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9) Select all correct statements about arctan.

Explanation

arctan(x) returns an angle θ such that tan(θ) = x, with θ ∈ (−π/2, π/2), and is defined for all real x.

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10) Solve θ = arctan(0). Which is the correct value for θ?

Explanation

tan(0) = 0, and 0 lies in the range (−π/2, π/2), so arctan(0) = 0.

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11) Evaluate arcsin(tan(arctan(2))). ____

Explanation

tan(arctan(2)) = 2, and arcsin(2) is not defined for real numbers as the value exceeds the range of arcsin. This statement isn't valid in the original form.

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12) The value of arctan(√2/2) is equal to ____.

Explanation

tan(π/4) = √2/2, so arctan(√2/2) = π/4.

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13) Arctan(x) is the inverse of tan(x) for all real values of x.

Explanation

arctan(x) is the inverse of the tangent function, and is defined for all real values of x, returning results in the range [−π/2, π/2].

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14) What is the range of the function y = arctan(x)?

Explanation

The range of arctan(x) is [−π/2, π/2] as it returns values in this interval only.

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15) What is the principal range of y = arctan(x)?

Explanation

The inverse tangent function is defined to return the angle θ in the interval [−π/2, π/2], where tan(θ) = x.

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16) For all real x, tan(arctan(x)) = x.

Explanation

Since tan and arctan are inverse functions, tan(arctan(x)) = x for all real x.

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17) Arctan(−1) = −π/4.

Explanation

Since tan(−π/4) = −1, arctan(−1) = −π/4.

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18) If θ = arctan(−√2), what is the value of θ in radians?

Explanation

tan(−π/3) = −√2, so arctan(−√2) = −π/3.

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19) Select all true statements for y = arctan(x).

Explanation

arctan(x) is defined for all real x, and it is an odd function. It is increasing and has a range of [−π/2, π/2], not [−π, π].

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20) What is the value of arctan(−1)?

Explanation

arctan(−1) is the angle where tan(θ) = −1, which is −π/4 within the principal range.

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Which of the following are true about the inverse tangent function?
For θ = arctan(x), the equation tan(θ) = x holds for all real values...
Arctan(−√3) = ____.
For y = arctan(x), the domain of this function is ____.
The function y = arctan(x) is increasing on its entire domain.
Select all correct definitions of arctan(x).
Select all true statements for y = arctan(x).
Arctan(1) = ____.
Select all correct statements about arctan.
Solve θ = arctan(0). Which is the correct value for θ?
Evaluate arcsin(tan(arctan(2))). ____
The value of arctan(√2/2) is equal to ____.
Arctan(x) is the inverse of tan(x) for all real values of x.
What is the range of the function y = arctan(x)?
What is the principal range of y = arctan(x)?
For all real x, tan(arctan(x)) = x.
Arctan(−1) = −π/4.
If θ = arctan(−√2), what is the value of θ in radians?
Select all true statements for y = arctan(x).
What is the value of arctan(−1)?
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