What is the general solution for (10.4)/(sin(x))=(12)/(sin(62)) ?

The general solution for (10.4)/(sin(x))=(12)/(sin(62)) is x=0.87138…+360n,x=180-0.87138…+360n

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(10.4)/(sin(x))=(12)/(sin(62))

\frac{10.4}{sin ( x )} = \frac{12}{sin ( 6 2 ^{\circ} )}

x = 0.87138 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.87138 \dots + 36 0^{\circ} n

Radians

x = 0.87138 \dots + 2 πn, x = π - 0.87138 \dots + 2 πn

Solution steps

\frac{10.4}{sin ( x )} = \frac{12}{sin ( 6 2 ^{\circ} )}

Cross multiply

\frac{10.4}{sin ( x )} = \frac{12}{sin ( 6 2 ^{\circ} )}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

10.4 sin (6 2^{\circ}) = sin (x) \cdot 12

10.4 sin (6 2^{\circ}) = sin (x) \cdot 12

Switch sides

sin (x) \cdot 12 = 10.4 sin (6 2^{\circ})

Divide both sides by

12

sin (x) \cdot 12 = 10.4 sin (6 2^{\circ})

Divide both sides by

12

\frac{sin ( x ) \cdot 12}{12} = \frac{10.4 sin ( 6 2 ^{\circ} )}{12}

Simplify

sin (x) = \frac{10.4 sin ( 6 2 ^{\circ} )}{12}

sin (x) = \frac{10.4 sin ( 6 2 ^{\circ} )}{12}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{10.4}{sin ( x )}

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{10.4 sin ( 6 2 ^{\circ} )}{12}

Apply trig inverse properties

sin (x) = \frac{10.4 sin ( 6 2 ^{\circ} )}{12}

General solutions for

sin (x) = \frac{10.4 sin ( 6 2 ^{\circ} )}{12}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{10.4 sin ( 6 2 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{10.4 sin ( 6 2 ^{\circ} )}{12}) + 36 0^{\circ} n

x = arcsin (\frac{10.4 sin ( 6 2 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{10.4 sin ( 6 2 ^{\circ} )}{12}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.87138 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.87138 \dots + 36 0^{\circ} n

csc (θ) = - 2, 0^{\circ} \leq θ \leq 36 0^{\circ}

sin (B) = \frac{12}{13}

csc (x - 4 5^{\circ}) = 2

- 5 sin (2 t) = 0

(cos (x) - 1) = 0

What is the general solution for (10.4)/(sin(x))=(12)/(sin(62)) ?
The general solution for (10.4)/(sin(x))=(12)/(sin(62)) is x=0.87138…+360n,x=180-0.87138…+360n