What is the general solution for sin(c)=(5sin(140))/7 ?

The general solution for sin(c)=(5sin(140))/7 is c=0.47702…+360n,c=180-0.47702…+360n

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sin(c)=(5sin(140))/7

sin (c) = \frac{5 sin ( 14 0 ^{\circ} )}{7}

c = 0.47702 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.47702 \dots + 36 0^{\circ} n

Radians

c = 0.47702 \dots + 2 πn, c = π - 0.47702 \dots + 2 πn

Solution steps

sin (c) = \frac{5 sin ( 14 0 ^{\circ} )}{7}

Apply trig inverse properties

sin (c) = \frac{5 sin ( 14 0 ^{\circ} )}{7}

General solutions for

sin (c) = \frac{5 sin ( 14 0 ^{\circ} )}{7}

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

c = arcsin (\frac{5 sin ( 14 0 ^{\circ} )}{7}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{5 sin ( 14 0 ^{\circ} )}{7}) + 36 0^{\circ} n

c = arcsin (\frac{5 sin ( 14 0 ^{\circ} )}{7}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{5 sin ( 14 0 ^{\circ} )}{7}) + 36 0^{\circ} n

Show solutions in decimal form

c = 0.47702 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.47702 \dots + 36 0^{\circ} n

7 = 5 sin (θ) + 2

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0, θ

2 (sin^{2} (x)) + 5 sin (x) - 3 = 0

cos^{2} (3 x) - sin^{2} (3 x) = - 1

x, arctan (\frac{y}{x}) = \frac{π}{4}

What is the general solution for sin(c)=(5sin(140))/7 ?
The general solution for sin(c)=(5sin(140))/7 is c=0.47702…+360n,c=180-0.47702…+360n