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

The general solution for 3+sin(x)=2 is x=(3pi)/2+2pin

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3+sin(x)=2

3 + sin (x) = 2

x = \frac{3 π}{2} + 2 πn

Degrees

x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

3 + sin (x) = 2

Move

3

to the right side

3 + sin (x) = 2

Subtract

3

from both sides

3 + sin (x) - 3 = 2 - 3

Simplify

sin (x) = - 1

sin (x) = - 1

General solutions for

sin (x) = - 1

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{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

1 - sin (A) cos (A) = (sin (A) - cos (A))^{2}

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

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

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

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

What is the general solution for 3+sin(x)=2 ?
The general solution for 3+sin(x)=2 is x=(3pi)/2+2pin