Show that sin &#x2061;<!-- ⁡ --> ( &#x03C0;<!-- π --> 12 </

auto23652im

auto23652im

Answered question

2022-07-07

Show that sin ( π 12 ) > 1 4

Answer & Explanation

talhekh

talhekh

Beginner2022-07-08Added 15 answers

If one can use sin π 6 = 1 2 , the double-angle formula gives
sin π 12 = sin π 6 2 cos π 12 = 1 4 cos π 12 ,
and all that remains is to argue that 0 < cos π 12 < 1
Augustus Acevedo

Augustus Acevedo

Beginner2022-07-09Added 4 answers

cos π 12 < 1 sin π 12 cos π 12 < sin π 12 1 2 ( 2 sin π 12 cos π 12 ) < sin π 12 1 2 sin π 6 < sin π 12 1 4 < sin π 12

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