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Inverse trig functions
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The inverse trig functions \(\arcsin\), \(\arccos\) and \(\arctan\), including their principal-value domains and ranges and the graphs as reflections of the restricted trig functions in \(y=x\).
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Inverse Sine (arcsin) Function
AHL 3.9
The inverse of sin is arcsin, also written sin−1. Its domain is the range of sin: (−1,1), and its range is the domain of sinx, restricted so that the inverse function passes the vertical line test: [−2π,2π].
The graph of y=arcsinx is the mirror image of sinx (restricted to −2π<x<2π) in the line y=x, giving an increasing function:
Inverse Cosine (arccos) Function
AHL 3.9
The inverse of cos is arccos, also written cos−1. Its domain is the range of cos: (−1,1), and its range is the domain of cosx, restricted so that the inverse function passes the vertical line test: [0,π].
The graph of y=arccosx is the mirror image of cosx (restricted to 0<x<π) in the line y=x, giving a decreasing function:
Inverse Tan (arctan) Function
AHL 3.9
The inverse of tan is arctan, also written tan−1. Its domain is the range of tan: all real numbers, and its range is the domain of tanx, restricted so that the inverse function passes the vertical line test: (−2π,2π).
The graph of y=arctanx is the mirror image of sinx (restricted to −2π<x<2π) in the line y=x, giving an increasing function:
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