What is the general solution for (sin(80))/5 =(sin(x))/4 ,x*(180)/pi =y ?

The general solution for (sin(80))/5 =(sin(x))/4 ,x*(180)/pi =y is No Solution for x\in\mathbb{R}

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(sin(80))/5 =(sin(x))/4 ,x*(180)/pi =y

\frac{sin ( 8 0 ^{\circ} )}{5} = \frac{sin ( x )}{4}, x \cdot \frac{180}{π} = y

No Solution for x \in R

Solution steps

\frac{sin ( 8 0 ^{\circ} )}{5} = \frac{sin ( x )}{4}, x \frac{180}{π} = y

Switch sides

\frac{sin ( x )}{4} = \frac{sin ( 8 0 ^{\circ} )}{5}

Multiply both sides by

4

sin (x) = \frac{4 sin ( 8 0 ^{\circ} )}{5}

Apply trig inverse properties

x = arcsin (\frac{4 sin ( 8 0 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 8 0 ^{\circ} )}{5}) + 36 0^{\circ} n

Solutions for the range

x \frac{180}{18 0 ^{\circ}} = y

No Solution for x \in R

6 sin^{2} (x) - 3 = 0

sin^{2} (x) = 2 cos (x) - 1

cos (x^{3}) = 0

2 cos^{2} (θ) = sin (θ) + 1

x, 2 = sec (x)

What is the general solution for (sin(80))/5 =(sin(x))/4 ,x*(180)/pi =y ?
The general solution for (sin(80))/5 =(sin(x))/4 ,x*(180)/pi =y is No Solution for x\in\mathbb{R}