What is the general solution for sin((3x)/2+45)=0 ?

The general solution for sin((3x)/2+45)=0 is x=(720n)/3-30,x=-30+120+(720n)/3

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sin((3x)/2+45)=0

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}, x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

Solution steps

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

General solutions for

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

\frac{3 x}{2} + 4 5^{\circ} = 0 + 36 0^{\circ} n, \frac{3 x}{2} + 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

Solve

\frac{3 x}{2} + 4 5^{\circ} = 0 + 36 0^{\circ} n : x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

Solve

\frac{3 x}{2} + 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n : x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}, x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

4 sin (2 θ) - 5 sin (θ) = 0

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

tan (\frac{2 x}{3}) - 1 = 0

sin (θ) - cos (θ) = 1

- \frac{5}{2} csc (\frac{θ}{2}) = - 3 - csc (\frac{θ}{2})

What is the general solution for sin((3x)/2+45)=0 ?
The general solution for sin((3x)/2+45)=0 is x=(720n)/3-30,x=-30+120+(720n)/3