What is the general solution for (sin(95))/(27)=(sin(b))/(16) ?

The general solution for (sin(95))/(27)=(sin(b))/(16) is b=0.63147…+360n,b=180-0.63147…+360n

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(sin(95))/(27)=(sin(b))/(16)

\frac{sin ( 9 5 ^{\circ} )}{27} = \frac{sin ( b )}{16}

b = 0.63147 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.63147 \dots + 36 0^{\circ} n

Radians

b = 0.63147 \dots + 2 πn, b = π - 0.63147 \dots + 2 πn

Solution steps

\frac{sin ( 9 5 ^{\circ} )}{27} = \frac{sin ( b )}{16}

Switch sides

\frac{sin ( b )}{16} = \frac{sin ( 9 5 ^{\circ} )}{27}

Multiply both sides by

16

\frac{sin ( b )}{16} = \frac{sin ( 9 5 ^{\circ} )}{27}

Multiply both sides by

16

\frac{16 sin ( b )}{16} = \frac{16 sin ( 9 5 ^{\circ} )}{27}

Simplify

sin (b) = \frac{16 sin ( 9 5 ^{\circ} )}{27}

sin (b) = \frac{16 sin ( 9 5 ^{\circ} )}{27}

Apply trig inverse properties

sin (b) = \frac{16 sin ( 9 5 ^{\circ} )}{27}

General solutions for

sin (b) = \frac{16 sin ( 9 5 ^{\circ} )}{27}

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

b = arcsin (\frac{16 sin ( 9 5 ^{\circ} )}{27}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{16 sin ( 9 5 ^{\circ} )}{27}) + 36 0^{\circ} n

b = arcsin (\frac{16 sin ( 9 5 ^{\circ} )}{27}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{16 sin ( 9 5 ^{\circ} )}{27}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.63147 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.63147 \dots + 36 0^{\circ} n

cos (x) + \frac{3}{2} = 0, 0 \leq x \leq 2 π

sinh (x) = \frac{12}{35}

sin^{2} (x) + \frac{1}{sec ( x )} = \frac{5}{4}

2 cos (\frac{1}{5} θ) = 3

sec (θ) = - \frac{7}{13}

What is the general solution for (sin(95))/(27)=(sin(b))/(16) ?
The general solution for (sin(95))/(27)=(sin(b))/(16) is b=0.63147…+360n,b=180-0.63147…+360n