What is the general solution for 1+2*sin(x)=2 ?

The general solution for 1+2*sin(x)=2 is x= pi/6+2pin,x=(5pi)/6+2pin

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1+2*sin(x)=2

1 + 2 \cdot sin (x) = 2

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

1 + 2 sin (x) = 2

Move

1

to the right side

1 + 2 sin (x) = 2

Subtract

1

from both sides

1 + 2 sin (x) - 1 = 2 - 1

Simplify

2 sin (x) = 1

2 sin (x) = 1

Divide both sides by

2

2 sin (x) = 1

Divide both sides by

2

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

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

1 + 2 \cdot sin (x) = 3

sin (α) = \frac{120 sin ( 6 0 ^{\circ} )}{1200}

15.8 \cdot sin (30 x - 90) + 5 = 17

2 sin^{(2)} (x) - sin (x) - 1 = 0

cos^{2} (θ) - 1 = sin^{2} (θ)

What is the general solution for 1+2*sin(x)=2 ?
The general solution for 1+2*sin(x)=2 is x= pi/6+2pin,x=(5pi)/6+2pin