Question

For 0°<θ<90°, the maximum value of 2/[3+sin^(2)θ] is ___?

Answer 1

\[\frac{ 2 }{ 3+\sin ^{2} \theta }\]

Answer 2

What value of theta makes this denominator have its smallest possible value over the interval [0,90] ? In short, at what value of theta is sin^(2)θ a minimum over the given interval?

Denominator: [3+sin^(2)θ]

Answer 3

for the given function to be maximum sin theta shuld be minimum

Answer 4

anyone can help :)

Answer 5

30°?

Answer 6

in the interval, 0°<θ<90°,
you say sin is minimum at 30 ??
please reconsider....

Answer 7

isn't the max?

Answer 8

wait, i don't understand the denominator

Answer 9

to get maximum value of 2/[3+sin^(2)θ] , you'll need minimum of denominator [3+sin^(2)θ] , right ?

Answer 10

yeah

Answer 11

60?

Answer 12

to get minimum of denominator [3+sin^(2)θ]
you need minimum of sin^2 theta, right ?

Answer 13

yes

Answer 14

so what is minimum of sin in the interval 0°<θ<90°, ?

Answer 15

1......?

Answer 16

umm, at start i have the answer 1/2 but i don't know is it correct

Answer 17

what about 0 degrees, what is sin 0 ?
is that minimum ?

Answer 18

0°<θ<90°
not 0°≤θ<90°

Answer 19

sin0° = 0

Answer 20

ok, but theta can be very very near to 0, denoted by
\(\theta \rightarrow 0^+\)
which means, theta \(\ne0\) but very near to 0 and greater than 0.
so, you can use the value of theta = 0 to find the minimum

Answer 21

then just put sin theta =0 in your expression...

Answer 22

2/3?

Answer 23

yes :)

Answer 24

thank you @hartnn :)