What is the general solution for sin(x)=sin(50) ?

The general solution for sin(x)=sin(50) is x=0.87266…+360n,x=180-0.87266…+360n

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sin(x)=sin(50)

sin (x) = sin (5 0^{\circ})

x = 0.87266 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.87266 \dots + 36 0^{\circ} n

Radians

x = 0.87266 \dots + 2 πn, x = π - 0.87266 \dots + 2 πn

Solution steps

sin (x) = sin (5 0^{\circ})

Apply trig inverse properties

sin (x) = sin (5 0^{\circ})

General solutions for

sin (x) = sin (5 0^{\circ})

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (sin (5 0^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (sin (5 0^{\circ})) + 36 0^{\circ} n

x = arcsin (sin (5 0^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (sin (5 0^{\circ})) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.87266 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.87266 \dots + 36 0^{\circ} n

n, y = - sin (2 (\frac{3 π}{4} + πn)) 2

tan (θ) = \frac{18}{7}

2 cos^{2} (θ) = 1 + sin (θ)

3 tan (x) = sin (x)

5 = sinh (x)

What is the general solution for sin(x)=sin(50) ?
The general solution for sin(x)=sin(50) is x=0.87266…+360n,x=180-0.87266…+360n