the sine function is an odd function, for a negative number u , sin ⁡ 2 u = − 2 sin ⁡ u cos ⁡ u. Is it true or false and why?

Question

the sine function is an odd function, for a negative number   u  ,  sin  ⁡  2  u  =  −  2  sin  ⁡  u  cos  ⁡  u. Is it true or false and why?

Sawyer Day · Accepted Answer

False.  sin  ⁡  2  u  =  2  sin  ⁡  u  cos  ⁡  u is an identity, true for any   u. If   u  &amp;lt;  0, write   u  =  −  x where   x  &amp;gt;  0. Then  sin  ⁡  2  u  =  sin  ⁡  (  −  2  x  )  =  −  sin  ⁡  (  2  x  )  =  −  2  sin  ⁡  x  cos  ⁡  x  =  −  2  sin  ⁡  (  −  u  )  cos  ⁡  (  −  u  )  =  2  sin  ⁡  u  cos  ⁡  uwhere the second and final steps follow since   sin is odd and   cos is even.

minwaardekn · Accepted Answer

It is false. The formula   sin  ⁡  (  2  u  )  =  2  sin  ⁡  u  cos  ⁡  u holds for all   u  ∈  R

the sine function is an odd function, for a negative number u , sin ⁡ 2

Answered question

Answer & Explanation

New Questions in Pre-Algebra