What is the general solution for (sin(160))/5 =(sin(c))/4 ?

The general solution for (sin(160))/5 =(sin(c))/4 is c=0.27715…+360n,c=180-0.27715…+360n

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(sin(160))/5 =(sin(c))/4

\frac{sin ( 16 0 ^{\circ} )}{5} = \frac{sin ( c )}{4}

c = 0.27715 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.27715 \dots + 36 0^{\circ} n

Radians

c = 0.27715 \dots + 2 πn, c = π - 0.27715 \dots + 2 πn

Solution steps

\frac{sin ( 16 0 ^{\circ} )}{5} = \frac{sin ( c )}{4}

Switch sides

\frac{sin ( c )}{4} = \frac{sin ( 16 0 ^{\circ} )}{5}

Multiply both sides by

4

\frac{sin ( c )}{4} = \frac{sin ( 16 0 ^{\circ} )}{5}

Multiply both sides by

4

\frac{4 sin ( c )}{4} = \frac{4 sin ( 16 0 ^{\circ} )}{5}

Simplify

sin (c) = \frac{4 sin ( 16 0 ^{\circ} )}{5}

sin (c) = \frac{4 sin ( 16 0 ^{\circ} )}{5}

Apply trig inverse properties

sin (c) = \frac{4 sin ( 16 0 ^{\circ} )}{5}

General solutions for

sin (c) = \frac{4 sin ( 16 0 ^{\circ} )}{5}

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

c = arcsin (\frac{4 sin ( 16 0 ^{\circ} )}{5}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{4 sin ( 16 0 ^{\circ} )}{5}) + 36 0^{\circ} n

c = arcsin (\frac{4 sin ( 16 0 ^{\circ} )}{5}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{4 sin ( 16 0 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

c = 0.27715 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.27715 \dots + 36 0^{\circ} n

sin (x) + 2 = 0

sin (θ) = - \frac{24}{25}

cos (2 x) + 7 sin (x) - 4 = 0

tan (\frac{θ}{8}) + 3 = 0

sin (\frac{θ}{2}) - 1 = 0, 0 \leq θ \leq 2 π

What is the general solution for (sin(160))/5 =(sin(c))/4 ?
The general solution for (sin(160))/5 =(sin(c))/4 is c=0.27715…+360n,c=180-0.27715…+360n