What is the general solution for 1sin(40)=1.5sin(x) ?

The general solution for 1sin(40)=1.5sin(x) is x=0.44285…+360n,x=180-0.44285…+360n

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1sin(40)=1.5sin(x)

1 sin (4 0^{\circ}) = 1.5 sin (x)

x = 0.44285 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.44285 \dots + 36 0^{\circ} n

Solution steps

1 \cdot sin (4 0^{\circ}) = 1.5 sin (x)

Switch sides

1.5 sin (x) = 1 \cdot sin (4 0^{\circ})

Multiply:

1 \cdot sin (4 0^{\circ}) = sin (4 0^{\circ})

1.5 sin (x) = sin (4 0^{\circ})

Divide both sides by

1.5

sin (x) = \frac{sin ( 4 0 ^{\circ} )}{1.5}

Apply trig inverse properties

x = arcsin (\frac{sin ( 4 0 ^{\circ} )}{1.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 4 0 ^{\circ} )}{1.5}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.44285 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.44285 \dots + 36 0^{\circ} n

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What is the general solution for 1sin(40)=1.5sin(x) ?
The general solution for 1sin(40)=1.5sin(x) is x=0.44285…+360n,x=180-0.44285…+360n