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

First thing, your units *must* be radians. It doesn’t work otherwise. With that in mind, it entirely depends on the accuracy you want. To get an actual answer, you would need to specify the accuracy.

For example, if you want to approximate sin(x) as x with 90% accuracy, you can use that approximation up to nearly 45° (so in radians, sin(pi/4) is about 90% of pi/4).

If you want 95% accuracy, it works up to about pi/6, or 30°. If you want 99% accuracy, it only works up to about 14°, about 0.245 radians.