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Question Number 63747 by Tony Lin last updated on 08/Jul/19

$$Whatdoes{sin}^{-2}xmean?$$

Commented by MJS last updated on 08/Jul/19

$${\mathrm{that}}^{\prime }\mathrm{s}\mathrm{the}\mathrm{question}...$$$${\mathrm{we}}^{\prime }\mathrm{re}\mathrm{not}\mathrm{consequent}\mathrm{in}\mathrm{these}\mathrm{things}$$$$f^{-1}\left(x\right)\mathrm{means}\mathrm{the}\mathrm{inverse}\mathrm{function}\mathrm{of}f\left(x\right)$$$$\mathrm{some}\mathrm{people}\mathrm{use}$$$$f^1\left(x\right)=f^{\prime }\left(x\right)$$$$f^2\left(x\right)=f^{″}\left(x\right)$$$$...$$$$\mathrm{for}\mathrm{trigonometric}\mathrm{functions}\mathrm{usually}$$$${\sin }^{-1}x=\arcsin x$$$${\cos }^{-1}x=\arccos x$$$$...$$$$\mathrm{but}$$$${\sin }^{2}x={\left(\sin x\right)}^2$$$$...$$$$\mathrm{so}$$$${\sin }^{-2}x\mathrm{could}\mathrm{mean}\mathrm{different}\mathrm{things}$$$$\frac{1}{{\sin }^{2}x}$$$${\arcsin }^{2}x$$$$\frac{1}{{\left(\sin x\right)}^{″}}$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{shame}$$

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