What is the general solution for (sin(37))/(23)=(sin(x))/(21) ?

The general solution for (sin(37))/(23)=(sin(x))/(21) is x=0.58174…+360n,x=180-0.58174…+360n

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(sin(37))/(23)=(sin(x))/(21)

\frac{sin ( 3 7 ^{\circ} )}{23} = \frac{sin ( x )}{21}

x = 0.58174 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.58174 \dots + 36 0^{\circ} n

Radians

x = 0.58174 \dots + 2 πn, x = π - 0.58174 \dots + 2 πn

Solution steps

\frac{sin ( 3 7 ^{\circ} )}{23} = \frac{sin ( x )}{21}

Switch sides

\frac{sin ( x )}{21} = \frac{sin ( 3 7 ^{\circ} )}{23}

Multiply both sides by

21

\frac{sin ( x )}{21} = \frac{sin ( 3 7 ^{\circ} )}{23}

Multiply both sides by

21

\frac{21 sin ( x )}{21} = \frac{21 sin ( 3 7 ^{\circ} )}{23}

Simplify

sin (x) = \frac{21 sin ( 3 7 ^{\circ} )}{23}

sin (x) = \frac{21 sin ( 3 7 ^{\circ} )}{23}

Apply trig inverse properties

sin (x) = \frac{21 sin ( 3 7 ^{\circ} )}{23}

General solutions for

sin (x) = \frac{21 sin ( 3 7 ^{\circ} )}{23}

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

x = arcsin (\frac{21 sin ( 3 7 ^{\circ} )}{23}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{21 sin ( 3 7 ^{\circ} )}{23}) + 36 0^{\circ} n

x = arcsin (\frac{21 sin ( 3 7 ^{\circ} )}{23}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{21 sin ( 3 7 ^{\circ} )}{23}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.58174 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.58174 \dots + 36 0^{\circ} n

csc (x) = \frac{1}{3}

(cot (x) + 1) (3 tan (x) - 1) = 0

2 cos^{2} (x) + sin (x) - 1 = 0, 0 \leq x \leq 2 π

cos^{3} (x) = cos^{2} (x)

cos (θ) = - 0.8

What is the general solution for (sin(37))/(23)=(sin(x))/(21) ?
The general solution for (sin(37))/(23)=(sin(x))/(21) is x=0.58174…+360n,x=180-0.58174…+360n