What is the general solution for 1.5sin(30)=sin(x) ?

The general solution for 1.5sin(30)=sin(x) is x=0.84806…+360n,x=180-0.84806…+360n

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1.5sin(30)=sin(x)

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

x = 0.84806 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.84806 \dots + 36 0^{\circ} n

Solution steps

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

sin (3 0^{\circ}) = \frac{1}{2}

1.5 \cdot \frac{1}{2} = sin (x)

Switch sides

sin (x) = 1.5 \cdot \frac{1}{2}

Simplify

1.5 \cdot \frac{1}{2} : \frac{1.5}{2}

Apply trig inverse properties

x = arcsin (\frac{1.5}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{1.5}{2}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.84806 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.84806 \dots + 36 0^{\circ} n

3 sin (x) - 3 cos (x) = 6

tan (θ) = \frac{11}{100}

sin (x) = \frac{4}{41}

2 cos (x) - sin^{2} (x) = 0

sin (x) = - 1.1

What is the general solution for 1.5sin(30)=sin(x) ?
The general solution for 1.5sin(30)=sin(x) is x=0.84806…+360n,x=180-0.84806…+360n