What is the general solution for (sin(120))/(2.34)=(sin(θ))/(1.2) ?

The general solution for (sin(120))/(2.34)=(sin(θ))/(1.2) is θ=0.46018…+360n,θ=180-0.46018…+360n

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(sin(120))/(2.34)=(sin(θ))/(1.2)

\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

θ = 0.46018 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46018 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

sin (12 0^{\circ}) = \frac{3}{2}

\frac{\frac{3}{2}}{2.34} = \frac{sin ( θ )}{1.2}

Switch sides

\frac{sin ( θ )}{1.2} = \frac{\frac{3}{2}}{2.34}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{sin ( θ )}{1.2} = \frac{3}{2 \cdot 2.34}

Multiply the numbers:

2 \cdot 2.34 = 4.68

\frac{sin ( θ )}{1.2} = \frac{3}{4.68}

Multiply both sides by

1.2

sin (θ) = 0.44411 \dots

Apply trig inverse properties

θ = arcsin (0.44411 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.44411 \dots) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.46018 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46018 \dots + 36 0^{\circ} n

tan (x) = \frac{12}{50}

sin (x) - 2 sin (x) \cdot cos (x) = 0

(cos (x) - 1) (cos (x) + 1) = 0

sin (x) = cos (3 0^{\circ})

sec (θ) cos (θ) tan (θ) = 1

What is the general solution for (sin(120))/(2.34)=(sin(θ))/(1.2) ?
The general solution for (sin(120))/(2.34)=(sin(θ))/(1.2) is θ=0.46018…+360n,θ=180-0.46018…+360n