Inverse Trigonometric Functions - AP Precalculus
Card 1 of 30
Evaluate $\text{arctan}(1)$.
Evaluate $\text{arctan}(1)$.
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$\frac{\text{π}}{4}$. Since $\tan(\frac{\pi}{4}) = 1$.
$\frac{\text{π}}{4}$. Since $\tan(\frac{\pi}{4}) = 1$.
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What is $\text{arccos}(\frac{1}{2})$?
What is $\text{arccos}(\frac{1}{2})$?
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$\frac{\text{π}}{3}$. Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$.
$\frac{\text{π}}{3}$. Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$.
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Evaluate $\text{arccos}(1)$.
Evaluate $\text{arccos}(1)$.
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$0$. Since $\cos(0) = 1$.
$0$. Since $\cos(0) = 1$.
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What is the domain of the inverse cotangent function, $\text{arccot}(x)$?
What is the domain of the inverse cotangent function, $\text{arccot}(x)$?
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$(-\text{∞}, \text{∞})$. Cotangent is defined for all real numbers.
$(-\text{∞}, \text{∞})$. Cotangent is defined for all real numbers.
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Evaluate $\text{arccos}(1)$.
Evaluate $\text{arccos}(1)$.
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$0$. Since $\cos(0) = 1$.
$0$. Since $\cos(0) = 1$.
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Find the value of $\text{arctan}(-1)$.
Find the value of $\text{arctan}(-1)$.
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$-\frac{\text{π}}{4}$. Since $\tan(-\frac{\pi}{4}) = -1$.
$-\frac{\text{π}}{4}$. Since $\tan(-\frac{\pi}{4}) = -1$.
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Evaluate $\text{arcsec}(-2)$.
Evaluate $\text{arcsec}(-2)$.
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$\frac{2\text{π}}{3}$. Since $\sec(\frac{2\pi}{3}) = -2$ in quadrant II.
$\frac{2\text{π}}{3}$. Since $\sec(\frac{2\pi}{3}) = -2$ in quadrant II.
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Evaluate $\text{arctan}(0)$.
Evaluate $\text{arctan}(0)$.
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$0$. Since $\tan(0) = 0$.
$0$. Since $\tan(0) = 0$.
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Find $\text{arccos}(-\frac{\sqrt{3}}{2})$.
Find $\text{arccos}(-\frac{\sqrt{3}}{2})$.
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$\frac{5\pi}{6}$. Since $\cos(\frac{5\pi}{6}) = -\frac{\sqrt{3}}{2}$ in quadrant II.
$\frac{5\pi}{6}$. Since $\cos(\frac{5\pi}{6}) = -\frac{\sqrt{3}}{2}$ in quadrant II.
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What is the principal value of $\text{arcsec}(-1)$?
What is the principal value of $\text{arcsec}(-1)$?
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$\text{π}$. Since $\sec(\pi) = -1$.
$\text{π}$. Since $\sec(\pi) = -1$.
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What is the range of the inverse tangent function, $\text{arctan}(x)$?
What is the range of the inverse tangent function, $\text{arctan}(x)$?
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The range is $(-\frac{\text{π}}{2}, \frac{\text{π}}{2})$. Asymptotic limits as x approaches $±∞$.
The range is $(-\frac{\text{π}}{2}, \frac{\text{π}}{2})$. Asymptotic limits as x approaches $±∞$.
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What is the principal value of $\text{arccsc}(1)$?
What is the principal value of $\text{arccsc}(1)$?
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$\frac{\text{π}}{2}$. Since $\csc(\frac{\pi}{2}) = 1$.
$\frac{\text{π}}{2}$. Since $\csc(\frac{\pi}{2}) = 1$.
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Find $\text{arccot}(\text{√3})$.
Find $\text{arccot}(\text{√3})$.
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$\frac{\text{π}}{6}$. Since $\cot(\frac{\pi}{6}) = \sqrt{3}$.
$\frac{\text{π}}{6}$. Since $\cot(\frac{\pi}{6}) = \sqrt{3}$.
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Evaluate $\text{arccsc}(-2)$.
Evaluate $\text{arccsc}(-2)$.
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$-\frac{\text{π}}{6}$. Since $\csc(-\frac{\pi}{6}) = -2$.
$-\frac{\text{π}}{6}$. Since $\csc(-\frac{\pi}{6}) = -2$.
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What is the range of the inverse cotangent function, $\text{arccot}(x)$?
What is the range of the inverse cotangent function, $\text{arccot}(x)$?
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$(0, \text{π})$. Full range from 0 to $\pi$ for all real inputs.
$(0, \text{π})$. Full range from 0 to $\pi$ for all real inputs.
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What is the domain of the inverse secant function, $\text{arcsec}(x)$?
What is the domain of the inverse secant function, $\text{arcsec}(x)$?
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$(-\text{∞}, -1] \text{ or } [1, \text{∞})$. Secant undefined where cosine equals zero.
$(-\text{∞}, -1] \text{ or } [1, \text{∞})$. Secant undefined where cosine equals zero.
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What is the range of the inverse cosecant function, $\text{arccsc}(x)$?
What is the range of the inverse cosecant function, $\text{arccsc}(x)$?
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$[-\frac{\text{π}}{2}, 0) \text{ or } (0, \frac{\text{π}}{2}]$. Excludes 0 where cosecant is undefined.
$[-\frac{\text{π}}{2}, 0) \text{ or } (0, \frac{\text{π}}{2}]$. Excludes 0 where cosecant is undefined.
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Evaluate $\text{arccos}(-\frac{1}{2})$.
Evaluate $\text{arccos}(-\frac{1}{2})$.
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$\frac{2\text{π}}{3}$. Since $\cos(\frac{2\pi}{3}) = -\frac{1}{2}$ in quadrant II.
$\frac{2\text{π}}{3}$. Since $\cos(\frac{2\pi}{3}) = -\frac{1}{2}$ in quadrant II.
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Find $\text{arcsin}(-\frac{\text{√2}}{2})$.
Find $\text{arcsin}(-\frac{\text{√2}}{2})$.
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$-\frac{\text{π}}{4}$. Since $\sin(-\frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$.
$-\frac{\text{π}}{4}$. Since $\sin(-\frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$.
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What is the value of $\text{arccos}(0)$?
What is the value of $\text{arccos}(0)$?
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$\frac{\text{π}}{2}$. Since $\cos(\frac{\pi}{2}) = 0$.
$\frac{\text{π}}{2}$. Since $\cos(\frac{\pi}{2}) = 0$.
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Find $\text{arcsin}(-\frac{1}{2})$.
Find $\text{arcsin}(-\frac{1}{2})$.
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$-\frac{\text{π}}{6}$. Since $\sin(-\frac{\pi}{6}) = -\frac{1}{2}$.
$-\frac{\text{π}}{6}$. Since $\sin(-\frac{\pi}{6}) = -\frac{1}{2}$.
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What is $\text{arctan}(\text{√3})$?
What is $\text{arctan}(\text{√3})$?
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$\frac{\text{π}}{3}$. Since $\tan(\frac{\pi}{3}) = \sqrt{3}$.
$\frac{\text{π}}{3}$. Since $\tan(\frac{\pi}{3}) = \sqrt{3}$.
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What is $\text{arccos}(\frac{1}{2})$?
What is $\text{arccos}(\frac{1}{2})$?
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$\frac{\text{π}}{3}$. Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$.
$\frac{\text{π}}{3}$. Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$.
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What is $\text{arcsin}(\frac{1}{2})$?
What is $\text{arcsin}(\frac{1}{2})$?
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$\frac{\text{π}}{6}$. Since $\sin(\frac{\pi}{6}) = \frac{1}{2}$.
$\frac{\text{π}}{6}$. Since $\sin(\frac{\pi}{6}) = \frac{1}{2}$.
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Evaluate $\text{arctan}(1)$.
Evaluate $\text{arctan}(1)$.
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$\frac{\text{π}}{4}$. Since $\tan(\frac{\pi}{4}) = 1$.
$\frac{\text{π}}{4}$. Since $\tan(\frac{\pi}{4}) = 1$.
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Find the value of $\text{arctan}(-1)$.
Find the value of $\text{arctan}(-1)$.
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$-\frac{\text{π}}{4}$. Since $\tan(-\frac{\pi}{4}) = -1$.
$-\frac{\text{π}}{4}$. Since $\tan(-\frac{\pi}{4}) = -1$.
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Identify the principal value of $\text{arccos}(-1)$.
Identify the principal value of $\text{arccos}(-1)$.
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$\text{π}$. Since $\cos(\pi) = -1$.
$\text{π}$. Since $\cos(\pi) = -1$.
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Identify the principal value of $\text{arcsin}(-1)$.
Identify the principal value of $\text{arcsin}(-1)$.
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$-\frac{\text{π}}{2}$. Since $\sin(-\frac{\pi}{2}) = -1$.
$-\frac{\text{π}}{2}$. Since $\sin(-\frac{\pi}{2}) = -1$.
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Evaluate $\text{arcsec}(2)$.
Evaluate $\text{arcsec}(2)$.
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$\frac{\text{π}}{3}$. Since $\sec(\frac{\pi}{3}) = 2$.
$\frac{\text{π}}{3}$. Since $\sec(\frac{\pi}{3}) = 2$.
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What is the inverse of $\text{sin}(\theta) = x$?
What is the inverse of $\text{sin}(\theta) = x$?
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$\theta = \text{arcsin}(x)$. Solving for $\theta$ when sine equals $x$.
$\theta = \text{arcsin}(x)$. Solving for $\theta$ when sine equals $x$.
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