I have seen many times that for small angles sinθ≈θ, i want to know for how small value?

Question

and i think the value is less than 1 right? certainly sin1 ≠ 1. here units i used are degrees.

In: 6

Answer 1

The Taylor series for sin is sinx = x – x^(3)/3! + x^(5)/5! – x^(7)/7! +…

This means you can approximate sinx by taking a few elements from the series – the more elements you take, the more accurate the value. If you take just one element (x) then the error will be no more than |x^(3)|/3! so for example if x=1 then the error is no more than 1/6. Of course the larger x is, the larger the error.