What is the general solution for (sin(78)}{14}=\frac{sin(a))/6 ?

The general solution for (sin(78)}{14}=\frac{sin(a))/6 is a=0.43257…+360n,a=180-0.43257…+360n

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(sin(78)}{14}=\frac{sin(a))/6

\frac{sin ( 7 8 ^{\circ} )}{14} = \frac{sin ( a )}{6}

a = 0.43257 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.43257 \dots + 36 0^{\circ} n

Radians

a = 0.43257 \dots + 2 πn, a = π - 0.43257 \dots + 2 πn

Solution steps

\frac{sin ( 7 8 ^{\circ} )}{14} = \frac{sin ( a )}{6}

Switch sides

\frac{sin ( a )}{6} = \frac{sin ( 7 8 ^{\circ} )}{14}

Multiply both sides by

6

\frac{sin ( a )}{6} = \frac{sin ( 7 8 ^{\circ} )}{14}

Multiply both sides by

6

\frac{6 sin ( a )}{6} = \frac{6 sin ( 7 8 ^{\circ} )}{14}

Simplify

sin (a) = \frac{3 sin ( 7 8 ^{\circ} )}{7}

sin (a) = \frac{3 sin ( 7 8 ^{\circ} )}{7}

Apply trig inverse properties

sin (a) = \frac{3 sin ( 7 8 ^{\circ} )}{7}

General solutions for

sin (a) = \frac{3 sin ( 7 8 ^{\circ} )}{7}

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

a = arcsin (\frac{3 sin ( 7 8 ^{\circ} )}{7}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{3 sin ( 7 8 ^{\circ} )}{7}) + 36 0^{\circ} n

a = arcsin (\frac{3 sin ( 7 8 ^{\circ} )}{7}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{3 sin ( 7 8 ^{\circ} )}{7}) + 36 0^{\circ} n

Show solutions in decimal form

a = 0.43257 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.43257 \dots + 36 0^{\circ} n

tan (x) = (- \frac{6}{5})

cos (x^{2}) = 1

2 sin^{2} (θ) + cos (θ) - 2 = 0

sin^{3} (x) - 0.25 sin (x) = 0

sin^{2} (x) cos (x) = 0

What is the general solution for (sin(78)}{14}=\frac{sin(a))/6 ?
The general solution for (sin(78)}{14}=\frac{sin(a))/6 is a=0.43257…+360n,a=180-0.43257…+360n