What is the general solution for (10)/(sin(x))=(100)/(sin(90)) ?

The general solution for (10)/(sin(x))=(100)/(sin(90)) is x=0.10016…+360n,x=180-0.10016…+360n

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(10)/(sin(x))=(100)/(sin(90))

\frac{10}{sin ( x )} = \frac{100}{sin ( 9 0 ^{\circ} )}

x = 0.10016 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.10016 \dots + 36 0^{\circ} n

Solution steps

\frac{10}{sin ( x )} = \frac{100}{sin ( 9 0 ^{\circ} )}

sin (9 0^{\circ}) = 1

\frac{10}{sin ( x )} = \frac{100}{1}

Cross multiply

10 = sin (x) \cdot 100

Switch sides

sin (x) \cdot 100 = 10

Divide both sides by

100

sin (x) = \frac{1}{10}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{1}{10}

Apply trig inverse properties

x = arcsin (\frac{1}{10}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{1}{10}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.10016 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.10016 \dots + 36 0^{\circ} n

\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

tan (x) = \frac{12}{50}

sin (x) - 2 sin (x) \cdot cos (x) = 0

(cos (x) - 1) (cos (x) + 1) = 0

sin (x) = cos (3 0^{\circ})

What is the general solution for (10)/(sin(x))=(100)/(sin(90)) ?
The general solution for (10)/(sin(x))=(100)/(sin(90)) is x=0.10016…+360n,x=180-0.10016…+360n