Thursday, 5 July 2018

algebra precalculus - Approximation of the Sine function near 0



What is the reason that for x<0.5, sin(x)x?




Are there more known properties of these kind for other trigonometry functions?


Answer



To see that sin(x)x for small x all you have to do (without using the Taylor series) is look at the graph:
enter image description here



You can see that sinx=x when x=0, and since the gradient of the graph is approximately 1 for $-0.5

cosx1x22




tanxx


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