Write the maximum value 12 sin-9 sin 2-

12 sin θ 9 sin^2θ = 3 sin θ(4 3sin θ) We know that 0 ≤ sin θ≤ 1 ∴ Maximum value of 12 sin θ 9 sin^2θ = 12 ( 2/3 ) 9 ( 2/3 )^2 = 24/3 36/9 = 36/9 = 4 Because ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integration Using Substitution

Write the max...

Question

Write the maximum value $12 s i n θ - 9 s i n^{2} θ$ .

Open in App

Solution

$12 s i n θ - 9 s i n^{2} θ = 3 s i n θ (4 - 3 s i n θ)$
We know that $0 \leq s i n θ \leq 1$
$∴$ Maximum value of $12 s i n θ - 9 s i n^{2} θ$
$= 12 (\frac{2}{3}) - 9 {(\frac{2}{3})}^{2} = \frac{24}{3} - \frac{36}{9}$
$= \frac{36}{9} = 4$
Because for other than $s i n θ = \frac{4}{3}$ it is less than 4 maximum value of $12 s i n θ - s i n^{2} θ = 4$

Suggest Corrections

Write the maximum value 12sinθ−9sin2θ.

12sinθ−9sin2θ=3sinθ(4−3sinθ) We know that 0≤sinθ≤1 ∴ Maximum value of 12sinθ−9sin2θ =12(23)−9(23)2=243−369 =369=4 Because for other than sinθ=43 it is less than 4 maximum value of 12sinθ−sin2θ=4

Write the maximum value $12 s i n θ - 9 s i n^{2} θ$ .