What is the general solution for sin(θ)=-1,0<= θ<360 ?

The general solution for sin(θ)=-1,0<= θ<360 is θ=270

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sin(θ)=-1,0<= θ<360

sin (θ) = - 1, 0^{\circ} \leq θ < 36 0^{\circ}

θ = 27 0^{\circ}

Radians

θ = \frac{3 π}{2}

Solution steps

sin (θ) = - 1, 0^{\circ} \leq θ < 36 0^{\circ}

General solutions for

sin (θ) = - 1

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = 27 0^{\circ} + 36 0^{\circ} n

θ = 27 0^{\circ} + 36 0^{\circ} n

Solutions for the range

0 \leq θ < 36 0^{\circ}

θ = 27 0^{\circ}

sin (x) = 7

sin^{2} (x) cos^{2} (x) = \frac{2 - 2}{16}

(sin (x) - 1) (sin (x) - 5) = 0

csc (x) = \frac{5}{2}

csc (x) = \frac{5}{4}

What is the general solution for sin(θ)=-1,0<= θ<360 ?
The general solution for sin(θ)=-1,0<= θ<360 is θ=270