anonymous
  • anonymous
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?
Mathematics
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anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
x^2 + 1^2 = 1 ( just using the first terms for the series expansions ) this yields a small x fitting the series approximation
anonymous
  • anonymous
in other words is x is 0 in the limit then 1 = 1
anonymous
  • anonymous
Thanks

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