What is the general solution for sin(x)=sin(27) ?

The general solution for sin(x)=sin(27) is x=0.47123…+360n,x=180-0.47123…+360n

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sin(x)=sin(27)

sin (x) = sin (2 7^{\circ})

x = 0.47123 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.47123 \dots + 36 0^{\circ} n

Solution steps

sin (x) = sin (2 7^{\circ})

sin (2 7^{\circ}) = \frac{2 4 - 2 5 - 5}{4}

sin (x) = \frac{2 4 - 2 5 - 5}{4}

Apply trig inverse properties

x = arcsin \frac{2 4 - 2 5 - 5}{4} + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin \frac{2 4 - 2 5 - 5}{4} + 36 0^{\circ} n

Show solutions in decimal form

x = 0.47123 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.47123 \dots + 36 0^{\circ} n

cos (a) = \frac{12}{37}

120 sin (x - 12 0^{\circ}) = 120 sin (x - 24 0^{\circ})

sin^{2} (x) = 1 - sin^{2} (x)

- 8 cos (θ) = 43

2 sin (3 a) = - 1

What is the general solution for sin(x)=sin(27) ?
The general solution for sin(x)=sin(27) is x=0.47123…+360n,x=180-0.47123…+360n