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

The general solution for sin(x)+(sqrt(2))/2 =0 is x=(5pi)/4+2pin,x=(7pi)/4+2pin

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sin(x)+(sqrt(2))/2 =0

sin (x) + \frac{2}{2} = 0

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Degrees

x = 22 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) + \frac{2}{2} = 0

Move

\frac{2}{2}

to the right side

sin (x) + \frac{2}{2} = 0

Subtract

\frac{2}{2}

from both sides

sin (x) + \frac{2}{2} - \frac{2}{2} = 0 - \frac{2}{2}

Simplify

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

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

General solutions for

sin (x) = - \frac{2}{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{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

2 csc (θ) = 4 cos (θ)

\frac{6}{5} arccos (\frac{y}{6}) = π

cos (x) = \frac{154}{212.85}

4 sin^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

csc^{2} (θ) = 7 cot (θ) + 9

What is the general solution for sin(x)+(sqrt(2))/2 =0 ?
The general solution for sin(x)+(sqrt(2))/2 =0 is x=(5pi)/4+2pin,x=(7pi)/4+2pin