What is the general solution for (2.68)/(sin(126))=(1.2)/(sin(x)) ?

The general solution for (2.68)/(sin(126))=(1.2)/(sin(x)) is x=0.37067…+360n,x=180-0.37067…+360n

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(2.68)/(sin(126))=(1.2)/(sin(x))

\frac{2.68}{sin ( 12 6 ^{\circ} )} = \frac{1.2}{sin ( x )}

x = 0.37067 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.37067 \dots + 36 0^{\circ} n

Solution steps

\frac{2.68}{sin ( 12 6 ^{\circ} )} = \frac{1.2}{sin ( x )}

sin (12 6^{\circ}) = \frac{5 + 1}{4}

\frac{2.68}{\frac{5 + 1}{4}} = \frac{1.2}{sin ( x )}

Cross multiply

2.68 sin (x) = \frac{1.2 ( 5 + 1 )}{4}

Multiply both sides by

100

268 sin (x) = 30 (1 + 5)

Divide both sides by

268

sin (x) = \frac{15 ( 1 + 5 )}{134}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{15 ( 1 + 5 )}{134}

Apply trig inverse properties

x = arcsin (\frac{15 ( 1 + 5 )}{134}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{15 ( 1 + 5 )}{134}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.37067 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.37067 \dots + 36 0^{\circ} n

3 csc^{2} (x) - 5 csc (x) - 2 = 0

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

2 sin (x) cos (x) + cos (x) = 0, 0 \leq x \leq 2 π

a, sin (2 a) + 1 = 0.5

\frac{( sin ( 5 x ) )}{( - 1 cos ( 5 x ) )} = 0

What is the general solution for (2.68)/(sin(126))=(1.2)/(sin(x)) ?
The general solution for (2.68)/(sin(126))=(1.2)/(sin(x)) is x=0.37067…+360n,x=180-0.37067…+360n