What is the general solution for (sin(8))/(30)=(sin(θ))/(120) ?

The general solution for (sin(8))/(30)=(sin(θ))/(120) is No Solution for θ\in\mathbb{R}

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(sin(8))/(30)=(sin(θ))/(120)

\frac{sin ( 8 )}{30} = \frac{sin ( θ )}{120}

No Solution for θ \in R

Solution steps

\frac{sin ( 8 )}{30} = \frac{sin ( θ )}{120}

Switch sides

\frac{sin ( θ )}{120} = \frac{sin ( 8 )}{30}

Multiply both sides by

10

\frac{sin ( θ )}{120} = \frac{sin ( 8 )}{30}

Multiply both sides by

10

\frac{sin ( θ )}{120} \cdot 10 = \frac{sin ( 8 )}{30} \cdot 10

Simplify

\frac{sin ( θ )}{120} \cdot 10 = \frac{sin ( 8 )}{30} \cdot 10

Simplify

\frac{sin ( θ )}{120} \cdot 10 : \frac{sin ( θ )}{12}

\frac{sin ( θ )}{120} \cdot 10

Multiply fractions:

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

= \frac{sin ( θ ) \cdot 10}{120}

Cancel the common factor:

10

= \frac{sin ( θ )}{12}

Simplify

\frac{sin ( 8 )}{30} \cdot 10 : \frac{sin ( 8 )}{3}

\frac{sin ( 8 )}{30} \cdot 10

Multiply fractions:

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

= \frac{sin ( 8 ) \cdot 10}{30}

Cancel the common factor:

10

= \frac{sin ( 8 )}{3}

\frac{sin ( θ )}{12} = \frac{sin ( 8 )}{3}

\frac{sin ( θ )}{12} = \frac{sin ( 8 )}{3}

\frac{sin ( θ )}{12} = \frac{sin ( 8 )}{3}

Multiply both sides by

12

\frac{sin ( θ )}{12} = \frac{sin ( 8 )}{3}

Multiply both sides by

12

\frac{12 sin ( θ )}{12} = \frac{12 sin ( 8 )}{3}

Simplify

sin (θ) = 4 sin (8)

sin (θ) = 4 sin (8)

- 1 \leq sin (x) \leq 1

No Solution for θ \in R

What is the general solution for (sin(8))/(30)=(sin(θ))/(120) ?
The general solution for (sin(8))/(30)=(sin(θ))/(120) is No Solution for θ\in\mathbb{R}