Trigonometry's power (2)
Geometry
Level
3
Find the maximum value of the above expression.
The maximum does not exist
0
1/2016
2017/2016
1
2016/2017
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1 solution
2 0 1 6 sin 3 ( x ) + 2 0 1 7 sin 2 ( x ) + 2 0 1 7 sin ( x ) + 1 2 0 1 6 − cos 2 0 1 6 ( x )
( 2 0 1 6 sin ( x ) + 1 ) ( sin 2 ( x ) + sin ( x ) + 1 ) 2 0 1 6 − cos 2 0 1 6 ( x )
Put sin ( x ) = − 2 0 1 6 1 :
( − 1 + 1 ) ( ( − 2 0 1 6 1 ) 2 + ( − 2 0 1 6 1 ) + 1 ) 2 0 1 6 − cos 2 0 1 6 ( x )
0 2 0 1 6 − cos 2 0 1 6 ( x )
⇒ The maximum does not exist