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By means of straightforward methods, simple approximations are derived for the cosine, sine and tangent functions as well as for their inverse functions. The approximations are simple in the sense that they contain few terms and have numerical coefficients with, at most, three significant figures. The trigonometric approximations presented are valid in all four quadrants, including the singularity points in the case of the tangent. The inverse trigonometric approximations are valid over the full natural argument intervals. The absolute approximation errors are shown to be near-minimax with peak values all less than 0.25% of maximum. The results are expected to be useful in real-time signal processing circuits and systems where speed and simplicity rather than extreme accuracy are the dominating factors. A translinear circuit realisation example is given in the Appendix.