What is the general solution for (sin(48))/(13)=(sin(b))/(16) ?

The general solution for (sin(48))/(13)=(sin(b))/(16) is b=1.15461…+360n,b=180-1.15461…+360n

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(sin(48))/(13)=(sin(b))/(16)

\frac{sin ( 4 8 ^{\circ} )}{13} = \frac{sin ( b )}{16}

b = 1.15461 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 1.15461 \dots + 36 0^{\circ} n

Radians

b = 1.15461 \dots + 2 πn, b = π - 1.15461 \dots + 2 πn

Solution steps

\frac{sin ( 4 8 ^{\circ} )}{13} = \frac{sin ( b )}{16}

Switch sides

\frac{sin ( b )}{16} = \frac{sin ( 4 8 ^{\circ} )}{13}

Multiply both sides by

16

\frac{sin ( b )}{16} = \frac{sin ( 4 8 ^{\circ} )}{13}

Multiply both sides by

16

\frac{16 sin ( b )}{16} = \frac{16 sin ( 4 8 ^{\circ} )}{13}

Simplify

sin (b) = \frac{16 sin ( 4 8 ^{\circ} )}{13}

sin (b) = \frac{16 sin ( 4 8 ^{\circ} )}{13}

Apply trig inverse properties

sin (b) = \frac{16 sin ( 4 8 ^{\circ} )}{13}

General solutions for

sin (b) = \frac{16 sin ( 4 8 ^{\circ} )}{13}

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 ( 4 8 ^{\circ} )}{13}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{16 sin ( 4 8 ^{\circ} )}{13}) + 36 0^{\circ} n

b = arcsin (\frac{16 sin ( 4 8 ^{\circ} )}{13}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{16 sin ( 4 8 ^{\circ} )}{13}) + 36 0^{\circ} n

Show solutions in decimal form

b = 1.15461 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 1.15461 \dots + 36 0^{\circ} n

9 cos (2 θ) = 0

8 cos (θ) + 7 = - 6 cos (θ) + 5

8 sin (θ) + 15 cos (θ) = 17

8 sin (θ) + 15 cos (θ) = 14

cos (x - 1) = 0

What is the general solution for (sin(48))/(13)=(sin(b))/(16) ?
The general solution for (sin(48))/(13)=(sin(b))/(16) is b=1.15461…+360n,b=180-1.15461…+360n