If θ ∈[0,5 π] and r ∈ R such that 2 sin θ= r 4-2 r 2+3 then the maximum number of values of the pair ( r , θ) is

Question

If θ ∈[0,5 π] and r ∈ R such that 2 sin θ= r 4-2 r 2+3 then the maximum number of values of the pair ( r , θ) is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

2 sin θ=r4-2 r2+3 ⇒ 2 sin θ=(r2-1)2+2 This is possible only when sin θ=1 and r2=1 or r =± 1. So, θ=π / 2,5 π / 2,9 π / 2 ∴ Number of values of the pair (r, θ)=6

Q. If $θ \in [0, 5 π]$ and $r \in R$ such that $2 sin θ = r^{4} - 2 r^{2} + 3$ then the maximum number of values of the pair $(r, θ)$ is _______

$2 sin θ = r^{4} - 2 r^{2} + 3$
$\Rightarrow 2 sin θ = (r^{2} - 1)^{2} + 2$
This is possible only when $sin θ = 1$ and $r^{2} = 1$
or $r = \pm 1$ .
So, $θ = π /2, 5 π /2, 9 π /2$
$∴$ Number of values of the pair $(r, θ) = 6$

Q. If θ∈[0,5π] and r∈R such that 2sinθ=r4−2r2+3 then the maximum number of values of the pair (r,θ) is _______

2sinθ=r4−2r2+3 ⇒2sinθ=(r2−1)2+2 This is possible only when sinθ=1 and r2=1 or r=±1. So, θ=π/2,5π/2,9π/2 ∴ Number of values of the pair (r,θ)=6

Q. If $θ \in [0, 5 π]$ and $r \in R$ such that $2 sin θ = r^{4} - 2 r^{2} + 3$ then the maximum number of values of the pair $(r, θ)$ is _______

$2 sin θ = r^{4} - 2 r^{2} + 3$
$\Rightarrow 2 sin θ = (r^{2} - 1)^{2} + 2$
This is possible only when $sin θ = 1$ and $r^{2} = 1$
or $r = \pm 1$ .
So, $θ = π /2, 5 π /2, 9 π /2$
$∴$ Number of values of the pair $(r, θ) = 6$