What is the general solution for (sin(80))/5 =(sin(x))/4 ?

The general solution for (sin(80))/5 =(sin(x))/4 is x=0.90730…+360n,x=180-0.90730…+360n

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(sin(80))/5 =(sin(x))/4

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

x = 0.90730 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.90730 \dots + 36 0^{\circ} n

Solution steps

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

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

Show solutions in decimal form

x = 0.90730 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.90730 \dots + 36 0^{\circ} n

2 sin (2 x) + 1 = 0, 0 \leq x \leq 2 π

2 cos (θ) + 3 = 0

sin (x) + 2 = 0

2 sin (x) = 3

3 sin^{2} (θ) - 6 cos (θ) - 3 = - 4 cos (θ)

What is the general solution for (sin(80))/5 =(sin(x))/4 ?
The general solution for (sin(80))/5 =(sin(x))/4 is x=0.90730…+360n,x=180-0.90730…+360n