What is the general solution for 6sin(x)+12=15 ?

The general solution for 6sin(x)+12=15 is x= pi/6+2pin,x=(5pi)/6+2pin

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6sin(x)+12=15

6 sin (x) + 12 = 15

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

6 sin (x) + 12 = 15

Move

12

to the right side

6 sin (x) + 12 = 15

Subtract

12

from both sides

6 sin (x) + 12 - 12 = 15 - 12

Simplify

6 sin (x) = 3

6 sin (x) = 3

Divide both sides by

6

6 sin (x) = 3

Divide both sides by

6

\frac{6 sin ( x )}{6} = \frac{3}{6}

Simplify

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

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

What is the general solution for 6sin(x)+12=15 ?
The general solution for 6sin(x)+12=15 is x= pi/6+2pin,x=(5pi)/6+2pin