What is the general solution for (sin(78.05388889))/8 =(sin(x))/(10) ?

The general solution for (sin(78.05388889))/8 =(sin(x))/(10) is No Solution for x\in\mathbb{R}

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(sin(78.05388889))/8 =(sin(x))/(10)

\frac{sin ( 78.0538888 9 ^{\circ} )}{8} = \frac{sin ( x )}{10}

No Solution for x \in R

Solution steps

\frac{sin ( 78.05388 \dots ^{\circ} )}{8} = \frac{sin ( x )}{10}

Switch sides

\frac{sin ( x )}{10} = \frac{sin ( 78.05389 \dots ^{\circ} )}{8}

Multiply both sides by

10

\frac{sin ( x )}{10} = \frac{sin ( 78.05389 \dots ^{\circ} )}{8}

Multiply both sides by

10

\frac{sin ( x )}{10} \cdot 10 = \frac{sin ( 78.05389 \dots ^{\circ} )}{8} \cdot 10

Simplify

\frac{sin ( x )}{10} \cdot 10 = \frac{sin ( 78.05389 \dots ^{\circ} )}{8} \cdot 10

Simplify

\frac{sin ( x )}{10} \cdot 10 : sin (x)

\frac{sin ( x )}{10} \cdot 10

Multiply fractions:

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

= \frac{sin ( x ) \cdot 10}{10}

Cancel the common factor:

10

= sin (x)

Simplify

\frac{sin ( 78.05389 \dots ^{\circ} )}{8} \cdot 10 : \frac{5 sin ( 78.05389 \dots ^{\circ} )}{4}

\frac{sin ( 78.05389 \dots ^{\circ} )}{8} \cdot 10

Multiply fractions:

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

= \frac{sin ( 78.05389 \dots ^{\circ} ) \cdot 10}{8}

Cancel the common factor:

2

= \frac{5 sin ( 78.05389 \dots ^{\circ} )}{4}

sin (x) = \frac{5 sin ( 78.05389 \dots ^{\circ} )}{4}

sin (x) = \frac{5 sin ( 78.05389 \dots ^{\circ} )}{4}

sin (x) = \frac{5 sin ( 78.05389 \dots ^{\circ} )}{4}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

sin (x) = 32

88.2 sin (x) - 12.78 = 0.1 \cdot 88.2 cos (x)

1 + sin (x) = 2 \cdot cos (x)

sin (x) = 0.75 cos (x)

tan (x) = 1.15

What is the general solution for (sin(78.05388889))/8 =(sin(x))/(10) ?
The general solution for (sin(78.05388889))/8 =(sin(x))/(10) is No Solution for x\in\mathbb{R}