What is the general solution for (sin(70))/(25)=(sin(c))/(26) ?

The general solution for (sin(70))/(25)=(sin(c))/(26) is c=1.35722…+360n,c=180-1.35722…+360n

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(sin(70))/(25)=(sin(c))/(26)

\frac{sin ( 7 0 ^{\circ} )}{25} = \frac{sin ( c )}{26}

c = 1.35722 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 1.35722 \dots + 36 0^{\circ} n

Radians

c = 1.35722 \dots + 2 πn, c = π - 1.35722 \dots + 2 πn

Solution steps

\frac{sin ( 7 0 ^{\circ} )}{25} = \frac{sin ( c )}{26}

Switch sides

\frac{sin ( c )}{26} = \frac{sin ( 7 0 ^{\circ} )}{25}

Multiply both sides by

26

\frac{sin ( c )}{26} = \frac{sin ( 7 0 ^{\circ} )}{25}

Multiply both sides by

26

\frac{26 sin ( c )}{26} = \frac{26 sin ( 7 0 ^{\circ} )}{25}

Simplify

sin (c) = \frac{26 sin ( 7 0 ^{\circ} )}{25}

sin (c) = \frac{26 sin ( 7 0 ^{\circ} )}{25}

Apply trig inverse properties

sin (c) = \frac{26 sin ( 7 0 ^{\circ} )}{25}

General solutions for

sin (c) = \frac{26 sin ( 7 0 ^{\circ} )}{25}

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

c = arcsin (\frac{26 sin ( 7 0 ^{\circ} )}{25}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{26 sin ( 7 0 ^{\circ} )}{25}) + 36 0^{\circ} n

c = arcsin (\frac{26 sin ( 7 0 ^{\circ} )}{25}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{26 sin ( 7 0 ^{\circ} )}{25}) + 36 0^{\circ} n

Show solutions in decimal form

c = 1.35722 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 1.35722 \dots + 36 0^{\circ} n

\frac{csc ( x )}{2} = 3

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

1.25 sin (3 0^{\circ}) = 1.5 sin (x)

0 = - 3 sin (\frac{3}{4} x)

2 cos^{2} (θ) - 3 cos (θ) = 0, 0 \leq θ < 2 π

What is the general solution for (sin(70))/(25)=(sin(c))/(26) ?
The general solution for (sin(70))/(25)=(sin(c))/(26) is c=1.35722…+360n,c=180-1.35722…+360n