What is the general solution for (sin(51))/(18)=(sin(x))/(22) ?

The general solution for (sin(51))/(18)=(sin(x))/(22) is x=1.25274…+360n,x=180-1.25274…+360n

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(sin(51))/(18)=(sin(x))/(22)

\frac{sin ( 5 1 ^{\circ} )}{18} = \frac{sin ( x )}{22}

x = 1.25274 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.25274 \dots + 36 0^{\circ} n

Radians

x = 1.25274 \dots + 2 πn, x = π - 1.25274 \dots + 2 πn

Solution steps

\frac{sin ( 5 1 ^{\circ} )}{18} = \frac{sin ( x )}{22}

Switch sides

\frac{sin ( x )}{22} = \frac{sin ( 5 1 ^{\circ} )}{18}

Multiply both sides by

22

\frac{sin ( x )}{22} = \frac{sin ( 5 1 ^{\circ} )}{18}

Multiply both sides by

22

\frac{22 sin ( x )}{22} = \frac{22 sin ( 5 1 ^{\circ} )}{18}

Simplify

sin (x) = \frac{11 sin ( 5 1 ^{\circ} )}{9}

sin (x) = \frac{11 sin ( 5 1 ^{\circ} )}{9}

Apply trig inverse properties

sin (x) = \frac{11 sin ( 5 1 ^{\circ} )}{9}

General solutions for

sin (x) = \frac{11 sin ( 5 1 ^{\circ} )}{9}

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

x = arcsin (\frac{11 sin ( 5 1 ^{\circ} )}{9}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{11 sin ( 5 1 ^{\circ} )}{9}) + 36 0^{\circ} n

x = arcsin (\frac{11 sin ( 5 1 ^{\circ} )}{9}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{11 sin ( 5 1 ^{\circ} )}{9}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.25274 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.25274 \dots + 36 0^{\circ} n

3 (1 + sin (θ)) = 3 (1 - sin (θ))

cos (2 x) = sin (7 0^{\circ} + x)

tan (3 x) \cdot cot (x + 4 0^{\circ}) = 1

2 cos (θ) + 53 = 43

cos (x) = - \frac{1}{2} 2

What is the general solution for (sin(51))/(18)=(sin(x))/(22) ?
The general solution for (sin(51))/(18)=(sin(x))/(22) is x=1.25274…+360n,x=180-1.25274…+360n