What is the general solution for (sin(34))/(12)=(sin(x))/(15) ?

The general solution for (sin(34))/(12)=(sin(x))/(15) is x=0.77398…+360n,x=180-0.77398…+360n

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(sin(34))/(12)=(sin(x))/(15)

\frac{sin ( 3 4 ^{\circ} )}{12} = \frac{sin ( x )}{15}

x = 0.77398 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77398 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( 3 4 ^{\circ} )}{12} = \frac{sin ( x )}{15}

Switch sides

\frac{sin ( x )}{15} = \frac{sin ( 3 4 ^{\circ} )}{12}

Multiply both sides by

15

sin (x) = \frac{5 sin ( 3 4 ^{\circ} )}{4}

Apply trig inverse properties

x = arcsin (\frac{5 sin ( 3 4 ^{\circ} )}{4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 sin ( 3 4 ^{\circ} )}{4}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.77398 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.77398 \dots + 36 0^{\circ} n

3 - 3 cos (θ) = \frac{3}{2} sec (θ)

18 sec^{2} (x) - 3 tan (x) = 21

sin^{2} (θ) - 2 cos (θ) = 2

3 + 4 sin (θ) = 0

tan (2 A) = \frac{( 2 tan ( A ) )}{[ 1 + ( tan ( A ) ) ^{2} ]}

What is the general solution for (sin(34))/(12)=(sin(x))/(15) ?
The general solution for (sin(34))/(12)=(sin(x))/(15) is x=0.77398…+360n,x=180-0.77398…+360n