Oxford University MAT 2020 Solved Papers

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Question : 4 of 10

Marks: +1, -0

D. The largest value achieved by

3 \cos ^2 x+2 \sin x+1

equals

$\;{11}/{5}$ ,
$\;{13}/{3}$ ,
$\;{12}/{5}$ ,
$\;{14}/{9}$ ,
$\;{12}/{7}$ .

Solution:

3 \cos ^2 x+2 \sin x+1=3(1-\sin ^2 x)+2 \sin x+1=-3(\sin x-1 \/ 3)^2+1 \/ 3+4

. This takes its maximum value when

\sin x=1 \/ 3

, and that value is

4+1 \/ 3=13 \/ 3

.

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