What is the general solution for sin(x)=(16sin(31))/(12) ?

The general solution for sin(x)=(16sin(31))/(12) is x=0.75696…+360n,x=180-0.75696…+360n

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sin(x)=(16sin(31))/(12)

sin (x) = \frac{16 sin ( 3 1 ^{\circ} )}{12}

x = 0.75696 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.75696 \dots + 36 0^{\circ} n

Radians

x = 0.75696 \dots + 2 πn, x = π - 0.75696 \dots + 2 πn

Solution steps

sin (x) = \frac{16 sin ( 3 1 ^{\circ} )}{12}

Cancel the common factor:

4

sin (x) = \frac{4 sin ( 3 1 ^{\circ} )}{3}

Apply trig inverse properties

sin (x) = \frac{4 sin ( 3 1 ^{\circ} )}{3}

General solutions for

sin (x) = \frac{4 sin ( 3 1 ^{\circ} )}{3}

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

x = arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n

x = arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 1 ^{\circ} )}{3}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.75696 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.75696 \dots + 36 0^{\circ} n

sinh (z) - cosh (z) = 0

cos (x) = - 1.588908648

sin (- x) = 1

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

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

What is the general solution for sin(x)=(16sin(31))/(12) ?
The general solution for sin(x)=(16sin(31))/(12) is x=0.75696…+360n,x=180-0.75696…+360n