Find ordered pairs (x,θ) satisfying sinθ=|x|+1 when θ∈(0,π) .

sinθ=|x|+1 sinθ−1=|x| If θ=90° sin90°−1=|x| 0=|x| x=0 ∴ (0,π2) is ordered pair.

Find ordered pairs (x,θ) satisfying sinθ=|x|+1 when θ∈(0,π) .

sinθ=|x|+1 sinθ−1=|x| If θ=90° sin90°−1=|x| 0=|x| x=0 ∴ (0,π2) is ordered pair.

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Find ordered pairs $(x, θ)$ satisfying $\sin θ = | x | + 1$ when $θ \in (0, π)$ .

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(0, \frac{7 π}{2})

(0, \frac{π}{2})

(0, \frac{5 π}{2})

(0, - \frac{3 π}{2})

answer is A.

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Detailed Solution

\sin θ = | x | + 1

$\sin θ - 1 = | x |$

If $θ = 90 °$

$\sin 90 ° - 1 = | x |$

$0 = | x |$

$x = 0$

$∴$ $(0, \frac{π}{2})$ is ordered pair.

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Find ordered pairs $(x, θ)$ satisfying $\sin θ = | x | + 1$ when $θ \in (0, π)$ .