Question

what is the linear approximation of sin(0.11)?

I am confused because there is not a point on the unit circle that is close to that value? Where would I start?

Answer 1

in radians sin theta = theta for small angles
so if 0.11 is in radians then the answer is 0.11
however if it is 0.11 degrees, then you must convert
0.11 degrees * 3.14159 radians / 180 degrees = 0.001919 radians
so if degrees then sin 0.11 degrees = about 0.002

Answer 2

you want the tangent line at x = 0.11
since y' = cosx, that means you want the line
y - sin(0.11) = cos(0.11)(x - 0.11)
or, approximately
y - 0.11 = 0.994(x - 0.11)