What is the general solution for (sin(25))/5 =(sin(b))/8 ?

The general solution for (sin(25))/5 =(sin(b))/8 is b=0.74257…+360n,b=180-0.74257…+360n

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(sin(25))/5 =(sin(b))/8

\frac{sin ( 2 5 ^{\circ} )}{5} = \frac{sin ( b )}{8}

b = 0.74257 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.74257 \dots + 36 0^{\circ} n

Radians

b = 0.74257 \dots + 2 πn, b = π - 0.74257 \dots + 2 πn

Solution steps

\frac{sin ( 2 5 ^{\circ} )}{5} = \frac{sin ( b )}{8}

Switch sides

\frac{sin ( b )}{8} = \frac{sin ( 2 5 ^{\circ} )}{5}

Multiply both sides by

8

\frac{sin ( b )}{8} = \frac{sin ( 2 5 ^{\circ} )}{5}

Multiply both sides by

8

\frac{8 sin ( b )}{8} = \frac{8 sin ( 2 5 ^{\circ} )}{5}

Simplify

sin (b) = \frac{8 sin ( 2 5 ^{\circ} )}{5}

sin (b) = \frac{8 sin ( 2 5 ^{\circ} )}{5}

Apply trig inverse properties

sin (b) = \frac{8 sin ( 2 5 ^{\circ} )}{5}

General solutions for

sin (b) = \frac{8 sin ( 2 5 ^{\circ} )}{5}

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

b = arcsin (\frac{8 sin ( 2 5 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{8 sin ( 2 5 ^{\circ} )}{5}) + 36 0^{\circ} n

b = arcsin (\frac{8 sin ( 2 5 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{8 sin ( 2 5 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.74257 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.74257 \dots + 36 0^{\circ} n

cos (x) - cos (3 x) = - 2 sin (x)

sin (x) + sin (5 x) = 0

sin^{2} (x) + cos^{2} (x) = tan (x)

3 tan (3 x) = tan (x)

sin (x) = \frac{5}{5}, sin (2 x)

What is the general solution for (sin(25))/5 =(sin(b))/8 ?
The general solution for (sin(25))/5 =(sin(b))/8 is b=0.74257…+360n,b=180-0.74257…+360n