What is the general solution for sin(x)= 4/8 ?

The general solution for sin(x)= 4/8 is x= pi/6+2pin,x=(5pi)/6+2pin

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sin(x)= 4/8

sin (x) = \frac{4}{8}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{4}{8}

Cancel the common factor:

4

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

General solutions for

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

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (a) = - 1

sin^{2} (\frac{x}{2}) = \frac{1}{2 - ( \frac{1}{2} sin ( \frac{x}{2} ) )}

cos (x) - cos (x + \frac{π}{4}) = 0

cos (x) = 0.7597

cos (3 x) = - 3 cos (x)

What is the general solution for sin(x)= 4/8 ?
The general solution for sin(x)= 4/8 is x= pi/6+2pin,x=(5pi)/6+2pin