What is the general solution for (sin(57.22))/(31.5)=(sin(θ))/(24.4) ?

The general solution for (sin(57.22))/(31.5)=(sin(θ))/(24.4) is θ=0.70923…+360n,θ=180-0.70923…+360n

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(sin(57.22))/(31.5)=(sin(θ))/(24.4)

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( θ )}{24.4}

θ = 0.70923 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.70923 \dots + 36 0^{\circ} n

Radians

θ = 0.70923 \dots + 2 πn, θ = π - 0.70923 \dots + 2 πn

Solution steps

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( θ )}{24.4}

Switch sides

\frac{sin ( θ )}{24.4} = \frac{sin ( 57.2 2 ^{\circ} )}{31.5}

Multiply both sides by

24.4

\frac{sin ( θ )}{24.4} = \frac{sin ( 57.2 2 ^{\circ} )}{31.5}

Multiply both sides by

24.4

\frac{24.4 sin ( θ )}{24.4} = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

Simplify

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

Apply trig inverse properties

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

General solutions for

sin (θ) = \frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}

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

θ = arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n

θ = arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{24.4 sin ( 57.2 2 ^{\circ} )}{31.5}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.70923 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.70923 \dots + 36 0^{\circ} n

What is the general solution for (sin(57.22))/(31.5)=(sin(θ))/(24.4) ?
The general solution for (sin(57.22))/(31.5)=(sin(θ))/(24.4) is θ=0.70923…+360n,θ=180-0.70923…+360n