What is the general solution for (sin(74))/8 =(sin(a))/4 ?

The general solution for (sin(74))/8 =(sin(a))/4 is a=0.50137…+360n,a=180-0.50137…+360n

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(sin(74))/8 =(sin(a))/4

\frac{sin ( 7 4 ^{\circ} )}{8} = \frac{sin ( a )}{4}

a = 0.50137 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50137 \dots + 36 0^{\circ} n

Radians

a = 0.50137 \dots + 2 πn, a = π - 0.50137 \dots + 2 πn

Solution steps

\frac{sin ( 7 4 ^{\circ} )}{8} = \frac{sin ( a )}{4}

Switch sides

\frac{sin ( a )}{4} = \frac{sin ( 7 4 ^{\circ} )}{8}

Multiply both sides by

4

\frac{sin ( a )}{4} = \frac{sin ( 7 4 ^{\circ} )}{8}

Multiply both sides by

4

\frac{4 sin ( a )}{4} = \frac{4 sin ( 7 4 ^{\circ} )}{8}

Simplify

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

Apply trig inverse properties

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

General solutions for

sin (a) = \frac{sin ( 7 4 ^{\circ} )}{2}

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

a = arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n

a = arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{sin ( 7 4 ^{\circ} )}{2}) + 36 0^{\circ} n

Show solutions in decimal form

a = 0.50137 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50137 \dots + 36 0^{\circ} n

sin (x) = sin (x - \frac{π}{2})

tan (x) = \frac{π}{3}

- 7 tan (a) - 14 = tan (a) - 6

cos (x) = - 0.58

tan^{4} (x) - 4 tan^{2} (x) + 3 = 0

What is the general solution for (sin(74))/8 =(sin(a))/4 ?
The general solution for (sin(74))/8 =(sin(a))/4 is a=0.50137…+360n,a=180-0.50137…+360n