What is the general solution for (9.03)/(sin(40))=(10)/(sin(x)) ?

The general solution for (9.03)/(sin(40))=(10)/(sin(x)) is x=0.79210…+360n,x=180-0.79210…+360n

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(9.03)/(sin(40))=(10)/(sin(x))

\frac{9.03}{sin ( 4 0 ^{\circ} )} = \frac{10}{sin ( x )}

x = 0.79210 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.79210 \dots + 36 0^{\circ} n

Solution steps

\frac{9.03}{sin ( 4 0 ^{\circ} )} = \frac{10}{sin ( x )}

Cross multiply

9.03 sin (x) = sin (4 0^{\circ}) \cdot 10

Divide both sides by

9.03

sin (x) = \frac{sin ( 4 0 ^{\circ} ) \cdot 10}{9.03}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{sin ( 4 0 ^{\circ} ) \cdot 10}{9.03}

Apply trig inverse properties

x = arcsin (\frac{sin ( 4 0 ^{\circ} ) \cdot 10}{9.03}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 4 0 ^{\circ} ) \cdot 10}{9.03}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.79210 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.79210 \dots + 36 0^{\circ} n

tan (θ) (sec (θ) - 1) = 0

tan (x) + sec (x) = 2

sin (x) = \frac{4}{5}, \frac{π}{2} \leq x \leq π

2 - 2 cosh (t - 2) = 0

cos (x) = \frac{1}{37}

What is the general solution for (9.03)/(sin(40))=(10)/(sin(x)) ?
The general solution for (9.03)/(sin(40))=(10)/(sin(x)) is x=0.79210…+360n,x=180-0.79210…+360n