What is the general solution for sin(43.5)=1.5*sin(x) ?

The general solution for sin(43.5)=1.5*sin(x) is x=0.47676…+360n,x=180-0.47676…+360n

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sin(43.5)=1.5*sin(x)

sin (43. 5^{\circ}) = 1.5 \cdot sin (x)

x = 0.47676 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.47676 \dots + 36 0^{\circ} n

Radians

x = 0.47676 \dots + 2 πn, x = π - 0.47676 \dots + 2 πn

Solution steps

sin (43. 5^{\circ}) = 1.5 sin (x)

Switch sides

1.5 sin (x) = sin (43. 5^{\circ})

Divide both sides by

1.5

1.5 sin (x) = sin (43. 5^{\circ})

Divide both sides by

1.5

\frac{1.5 sin ( x )}{1.5} = \frac{sin ( 43. 5 ^{\circ} )}{1.5}

Simplify

sin (x) = \frac{sin ( 43. 5 ^{\circ} )}{1.5}

sin (x) = \frac{sin ( 43. 5 ^{\circ} )}{1.5}

Apply trig inverse properties

sin (x) = \frac{sin ( 43. 5 ^{\circ} )}{1.5}

General solutions for

sin (x) = \frac{sin ( 43. 5 ^{\circ} )}{1.5}

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

x = arcsin (\frac{sin ( 43. 5 ^{\circ} )}{1.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 43. 5 ^{\circ} )}{1.5}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 43. 5 ^{\circ} )}{1.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 43. 5 ^{\circ} )}{1.5}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.47676 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.47676 \dots + 36 0^{\circ} n

cos (x) = \frac{- 1}{10}

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

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

- 1 + sin (x) = - 1

\frac{2}{2} = sin (θ)

What is the general solution for sin(43.5)=1.5*sin(x) ?
The general solution for sin(43.5)=1.5*sin(x) is x=0.47676…+360n,x=180-0.47676…+360n