What is the general solution for (10)/(sin(x))=(13)/(sin(72)) ?

The general solution for (10)/(sin(x))=(13)/(sin(72)) is x=0.82063…+360n,x=180-0.82063…+360n

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(10)/(sin(x))=(13)/(sin(72))

\frac{10}{sin ( x )} = \frac{13}{sin ( 7 2 ^{\circ} )}

x = 0.82063 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.82063 \dots + 36 0^{\circ} n

Solution steps

\frac{10}{sin ( x )} = \frac{13}{sin ( 7 2 ^{\circ} )}

sin (7 2^{\circ}) = \frac{2 5 + 5}{4}

\frac{10}{sin ( x )} = \frac{13}{\frac{2 5 + 5}{4}}

Cross multiply

\frac{5 2 5 + 5}{2} = sin (x) \cdot 13

Switch sides

sin (x) \cdot 13 = \frac{5 2 5 + 5}{2}

Divide both sides by

13

sin (x) = \frac{5 2 5 + 5}{26}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{5 2 5 + 5}{26}

Apply trig inverse properties

x = arcsin (\frac{5 2 5 + 5}{26}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 2 5 + 5}{26}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.82063 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.82063 \dots + 36 0^{\circ} n

sin (x) - 3 cos (x) = 1, 0 \leq x < 2 π

sin (α) + 1 = cos (α)

\frac{sin ( 11 5 ^{\circ} )}{53} = \frac{sin ( S )}{83}

2 cos (x) - tan (x) = 0

0 = 3 sin (x)

What is the general solution for (10)/(sin(x))=(13)/(sin(72)) ?
The general solution for (10)/(sin(x))=(13)/(sin(72)) is x=0.82063…+360n,x=180-0.82063…+360n