What is the general solution for (sin(S))/(53)=(sin(115))/(83) ?

The general solution for (sin(S))/(53)=(sin(115))/(83) is S=0.61716…+360n,S=180-0.61716…+360n

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(sin(S))/(53)=(sin(115))/(83)

\frac{sin ( S )}{53} = \frac{sin ( 11 5 ^{\circ} )}{83}

S = 0.61716 \dots + 36 0^{\circ} n, S = 18 0^{\circ} - 0.61716 \dots + 36 0^{\circ} n

Radians

S = 0.61716 \dots + 2 πn, S = π - 0.61716 \dots + 2 πn

Solution steps

\frac{sin ( S )}{53} = \frac{sin ( 11 5 ^{\circ} )}{83}

Multiply both sides by

53

\frac{sin ( S )}{53} = \frac{sin ( 11 5 ^{\circ} )}{83}

Multiply both sides by

53

\frac{53 sin ( S )}{53} = \frac{53 sin ( 11 5 ^{\circ} )}{83}

Simplify

sin (S) = \frac{53 sin ( 11 5 ^{\circ} )}{83}

sin (S) = \frac{53 sin ( 11 5 ^{\circ} )}{83}

Apply trig inverse properties

sin (S) = \frac{53 sin ( 11 5 ^{\circ} )}{83}

General solutions for

sin (S) = \frac{53 sin ( 11 5 ^{\circ} )}{83}

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

S = arcsin (\frac{53 sin ( 11 5 ^{\circ} )}{83}) + 36 0^{\circ} n, S = 18 0^{\circ} - arcsin (\frac{53 sin ( 11 5 ^{\circ} )}{83}) + 36 0^{\circ} n

S = arcsin (\frac{53 sin ( 11 5 ^{\circ} )}{83}) + 36 0^{\circ} n, S = 18 0^{\circ} - arcsin (\frac{53 sin ( 11 5 ^{\circ} )}{83}) + 36 0^{\circ} n

Show solutions in decimal form

S = 0.61716 \dots + 36 0^{\circ} n, S = 18 0^{\circ} - 0.61716 \dots + 36 0^{\circ} n

25 sin^{2} (x) - 10 sin (x) + 1 = 0

4 - 4 sin (θ) = 2

1 - 2 cos (x) = sin^{2} (x)

cos (x) = \frac{84}{98}

cos (\frac{3 θ}{2}) = \frac{1}{2}

What is the general solution for (sin(S))/(53)=(sin(115))/(83) ?
The general solution for (sin(S))/(53)=(sin(115))/(83) is S=0.61716…+360n,S=180-0.61716…+360n