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

Radians

θ = 0.46018 \dots + 2 πn, θ = π - 0.46018 \dots + 2 πn

Solution steps

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

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

sin (12 0^{\circ})

Use the following trivial identity:

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

sin (12 0^{\circ})

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}

= \frac{3}{2}

= \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

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

Multiply both sides by

1.2

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

Simplify

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

Simplify

\frac{1.2 sin ( θ )}{1.2} : sin (θ)

\frac{1.2 sin ( θ )}{1.2}

Cancel the common factor:

1.2

= sin (θ)

Simplify

\frac{1.2 3}{4.68} : 0.44411 \dots

\frac{1.2 3}{4.68}

Convert element to a decimal form

3 = 1.73205 \dots

= \frac{1.2 \cdot 1.73205 \dots}{4.68}

Multiply the numbers:

1.2 \cdot 1.73205 \dots = 2.07846 \dots

= \frac{2.07846 \dots}{4.68}

Divide the numbers:

\frac{2.07846 \dots}{4.68} = 0.44411 \dots

= 0.44411 \dots

sin (θ) = 0.44411 \dots

sin (θ) = 0.44411 \dots

sin (θ) = 0.44411 \dots

Apply trig inverse properties

sin (θ) = 0.44411 \dots

General solutions for

sin (θ) = 0.44411 \dots

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

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

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

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