What is the maximum value of cos^4(x)+sin^2(x)+cos(x), when x >= 0?

linnibell17591

linnibell17591

Answered question

2022-11-15

What is the maximum value of cos 4 ( x ) + sin 2 ( x ) + cos ( x ), when x 0?

Answer & Explanation

Houston Ochoa

Houston Ochoa

Beginner2022-11-16Added 19 answers

Some trig problems can be done with elementary algebra. Let cos x = v . Then
cos 4 x + sin 2 x + cos x = cos 4 x + ( 1 cos 2 x ) + cos x =
= 1 + v v 2 + v 4 = 1 + v v 2 ( 1 v 2 )
1 + v 2
because v 2 ( 1 v 2 ) = ( cos 2 x ) ( 1 sin 2 x ) 0 and because 1 + v = 1 + cos x 2.
Now if cos x = 1 then v = 1 and 1 + v v 2 + v 4 = 2.

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