What is the general solution for (sin(65))/5 =(sin(x))/4 ?

The general solution for (sin(65))/5 =(sin(x))/4 is x=0.81110…+360n,x=180-0.81110…+360n

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(sin(65))/5 =(sin(x))/4

\frac{sin ( 6 5 ^{\circ} )}{5} = \frac{sin ( x )}{4}

x = 0.81110 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.81110 \dots + 36 0^{\circ} n

Radians

x = 0.81110 \dots + 2 πn, x = π - 0.81110 \dots + 2 πn

Solution steps

\frac{sin ( 6 5 ^{\circ} )}{5} = \frac{sin ( x )}{4}

Switch sides

\frac{sin ( x )}{4} = \frac{sin ( 6 5 ^{\circ} )}{5}

Multiply both sides by

4

\frac{sin ( x )}{4} = \frac{sin ( 6 5 ^{\circ} )}{5}

Multiply both sides by

4

\frac{4 sin ( x )}{4} = \frac{4 sin ( 6 5 ^{\circ} )}{5}

Simplify

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

Apply trig inverse properties

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

General solutions for

sin (x) = \frac{4 sin ( 6 5 ^{\circ} )}{5}

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

x = arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n

x = arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 6 5 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.81110 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.81110 \dots + 36 0^{\circ} n

1.33 \cdot sin (6 0^{\circ}) = 1.52 \cdot sin (x)

tan (x) = - 3 cos (x) tan (x)

tan (x - \frac{π}{4}) = \frac{1}{6}

cos (2 x) - 2 sin (x) = 1

arccos (\frac{3}{2}) + arcsin (3 x) = \frac{π}{2}

What is the general solution for (sin(65))/5 =(sin(x))/4 ?
The general solution for (sin(65))/5 =(sin(x))/4 is x=0.81110…+360n,x=180-0.81110…+360n