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:
You can see that sinx=x when x=0, and since the gradient of the graph is approximately 1 for $-0.5
cosx≈1−x22
tanx≈x
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