Wat is de
maximale waarde
van
sin3 x . cos3 x   ?
A.   1
B.   \(\frac12\)
C.   \(\frac14\)
D.   \(\frac16\)
E.   \(\frac18\)
A    B    C    D    E

[ 5-5405 - op net sinds 17.4.13-(E)-18.7.2024 ]

Translation in   E N G L I S H

What is the maximum value of
(sin3x)( cos3x)   ?
A.   1
B.   \(\frac12\)
C.   \(\frac14\)
D.   \(\frac16\)
E.   \(\frac18\)

Oplossing - Solution

sin³ x.cos³ x = 1/8 .8.sin³ x.cos³ x = 1/8.(2.sin x.cos x)³ = 1/8(sin 2x)³
De maximale waarde van sin 2x is 1, van (sin 2x)³ dus ook.
De maximale waarde van  1/8(sin 2x)³  is dus 1/8
gricha