The infinite series for sinx, cosx, and -sinx tell us that for small angles, sinx is approximately x, and cosx is approximately (1-.5x^2). With these approximations, check that (sinx)^2 + (cosx)^2 is approximately 1. I am stuck. Maybe I am approaching it wrong. Any hints?

Question

The infinite series for sinx, cosx, and -sinx tell us that for small angles, sinx is approximately x, and cosx is approximately (1-.5x^2).  With these approximations, check that (sinx)^2 + (cosx)^2 is approximately 1.  I am stuck.  Maybe I am approaching it wrong.  Any hints?

anonymous · Answer

x^2 + 1^2 = 1 ( just using the first terms for the series expansions )
this yields a small x fitting the series approximation

anonymous · Answer

in other words is x is 0 in the limit then 1 = 1

anonymous · Answer

Thanks