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Introduction

Small angle approximations allow us to estimate trigonometric functions like sine, cosine, and tangent, without a calculator. The angles involved must be small and in radians, usually at around 0.6 or less. There are three formulas to know: sine theta is approximately equal to theta, cos theta is approximately equal to 1 minus theta squared over 2, and tan theta is equal to theta. The idea is to use smaller values of theta for more accuracy, as larger values produce less reliable approximations. The reason why these approximations work is that for small angles, the graphs of y equals sine theta, y equals cosine theta and y equals tangent theta are almost the same as y equals theta.

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