What is the general solution for 1sin(30)=1.5sin(x) ?

The general solution for 1sin(30)=1.5sin(x) is x=0.33983…+360n,x=180-0.33983…+360n

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1sin(30)=1.5sin(x)

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

x = 0.33983 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.33983 \dots + 36 0^{\circ} n

Solution steps

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

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

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

Switch sides

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

Multiply both sides by

10

15 sin (x) = 5

Divide both sides by

15

sin (x) = \frac{1}{3}

Apply trig inverse properties

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

Show solutions in decimal form

x = 0.33983 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.33983 \dots + 36 0^{\circ} n

3 - 3 sin (t) = 33 cos (t)

sin (θ) = \frac{3}{10}

30 arctan (x) = 5 π

cosh (2 x) - 10 cosh (x) + 13 = 0

3 sin (x) - sin (2 x) = 0

What is the general solution for 1sin(30)=1.5sin(x) ?
The general solution for 1sin(30)=1.5sin(x) is x=0.33983…+360n,x=180-0.33983…+360n