What is the general solution for (30.56)/(sin(88))=(17)/(sin(x)) ?

The general solution for (30.56)/(sin(88))=(17)/(sin(x)) is x=0.58949…+360n,x=180-0.58949…+360n

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(30.56)/(sin(88))=(17)/(sin(x))

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

x = 0.58949 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.58949 \dots + 36 0^{\circ} n

Radians

x = 0.58949 \dots + 2 πn, x = π - 0.58949 \dots + 2 πn

Solution steps

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

Cross multiply

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

30.56 sin (x) = sin (8 8^{\circ}) \cdot 17

30.56 sin (x) = sin (8 8^{\circ}) \cdot 17

Divide both sides by

30.56

30.56 sin (x) = sin (8 8^{\circ}) \cdot 17

Divide both sides by

30.56

\frac{30.56 sin ( x )}{30.56} = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

Simplify

sin (x) = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

sin (x) = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{17}{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{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

Apply trig inverse properties

sin (x) = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

General solutions for

sin (x) = \frac{sin ( 8 8 ^{\circ} ) 17}{30.56}

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

x = arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.58949 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.58949 \dots + 36 0^{\circ} n

sec (x + \frac{π}{4}) = - 2, - π \leq x \leq π

\frac{56}{( 7.071 \cdot 7.681 )} = cos (θ)

tan (2 x + 1 0^{\circ}) = cot (x - 4 0^{\circ})

6 cos (2 t) = 0

2 cos^{2} (t) - 3 cos (t) = - 1, 0 \leq t \leq 2 π

What is the general solution for (30.56)/(sin(88))=(17)/(sin(x)) ?
The general solution for (30.56)/(sin(88))=(17)/(sin(x)) is x=0.58949…+360n,x=180-0.58949…+360n