What is the general solution for sin(x)=(6sin(20))/4 ?

The general solution for sin(x)=(6sin(20))/4 is x=0.53871…+360n,x=180-0.53871…+360n

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sin(x)=(6sin(20))/4

sin (x) = \frac{6 sin ( 2 0 ^{\circ} )}{4}

x = 0.53871 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.53871 \dots + 36 0^{\circ} n

Solution steps

sin (x) = \frac{6 sin ( 2 0 ^{\circ} )}{4}

Cancel the common factor:

2

sin (x) = \frac{3 sin ( 2 0 ^{\circ} )}{2}

Apply trig inverse properties

x = arcsin (\frac{3 sin ( 2 0 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 2 0 ^{\circ} )}{2}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.53871 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.53871 \dots + 36 0^{\circ} n

0 = 1.2209 \cdot cos (x) + 0.0422 \cdot cos (2 \cdot x)

5 sin (θ) + 3 = 0

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

cos (x) + cos (2 x) = - 1

cos (θ) = \frac{6}{3 5}

What is the general solution for sin(x)=(6sin(20))/4 ?
The general solution for sin(x)=(6sin(20))/4 is x=0.53871…+360n,x=180-0.53871…+360n