5.8 Inverse trigonometric functions
Arcsine
\(y=\arcsin{x} \iff \sin{y}=x\)
Domain: \(-1≤x≤1 \quad\) Range: \(-\dfrac{\pi}{2}≤y≤\dfrac{\pi}{2}\)
Arccosine
\(y=\arccos{x} \iff \cos{y}=x\)
Domain: \(-1≤x≤1 \quad\) Range: \(0≤y≤\pi\)
Arctangent
\(y=\arctan{x} \iff \tan{y}=x\)
Domain: \(-\dfrac{\pi}{2}≤y≤\dfrac{\pi}{2} \quad\) Range: \(y∈ℝ\)
\(y=\arcsin{x} \iff \sin{y}=x\)
Domain: \(-1≤x≤1 \quad\) Range: \(-\dfrac{\pi}{2}≤y≤\dfrac{\pi}{2}\)
Arccosine
\(y=\arccos{x} \iff \cos{y}=x\)
Domain: \(-1≤x≤1 \quad\) Range: \(0≤y≤\pi\)
Arctangent
\(y=\arctan{x} \iff \tan{y}=x\)
Domain: \(-\dfrac{\pi}{2}≤y≤\dfrac{\pi}{2} \quad\) Range: \(y∈ℝ\)
Important
Inverse trigonometric functions
\(y=\arcsin{x} \iff \sin{y}=x\)
\(y=\arccos{x} \iff \cos{y}=x\)
\(y=\arctan{x} \iff \tan{y}=x\)
\(y=\arcsin{x} \iff \sin{y}=x\)
\(y=\arccos{x} \iff \cos{y}=x\)
\(y=\arctan{x} \iff \tan{y}=x\)
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