What is the general solution for (sin(51))/(18)=(sin(c))/(17) ?

The general solution for (sin(51))/(18)=(sin(c))/(17) is c=0.82415…+360n,c=180-0.82415…+360n

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(sin(51))/(18)=(sin(c))/(17)

\frac{sin ( 5 1 ^{\circ} )}{18} = \frac{sin ( c )}{17}

c = 0.82415 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.82415 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( 5 1 ^{\circ} )}{18} = \frac{sin ( c )}{17}

Switch sides

\frac{sin ( c )}{17} = \frac{sin ( 5 1 ^{\circ} )}{18}

Multiply both sides by

17

sin (c) = \frac{17 sin ( 5 1 ^{\circ} )}{18}

Apply trig inverse properties

c = arcsin (\frac{17 sin ( 5 1 ^{\circ} )}{18}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{17 sin ( 5 1 ^{\circ} )}{18}) + 36 0^{\circ} n

Show solutions in decimal form

c = 0.82415 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.82415 \dots + 36 0^{\circ} n

0 = \frac{1}{2} cos (82 t) + \frac{1}{8} sin (82 t)

tan (θ) = - \frac{15}{8}

3 cos (x) cot (x) + 7 = 5 csc (x)

- 10 sin (2 x) = 0

sec (x) sin (x) - 3 sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

What is the general solution for (sin(51))/(18)=(sin(c))/(17) ?
The general solution for (sin(51))/(18)=(sin(c))/(17) is c=0.82415…+360n,c=180-0.82415…+360n