What is the general solution for sqrt(2)sin(x+pi/4)=0 ?

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

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sqrt(2)sin(x+pi/4)=0

2 sin (x + \frac{π}{4}) = 0

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

Degrees

x = - 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

2 sin (x + \frac{π}{4}) = 0

Divide both sides by

2

2 sin (x + \frac{π}{4}) = 0

Divide both sides by

2

\frac{2 sin ( x + \frac{π}{4} )}{2} = \frac{0}{2}

Simplify

sin (x + \frac{π}{4}) = 0

sin (x + \frac{π}{4}) = 0

General solutions for

sin (x + \frac{π}{4}) = 0

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}{4} = 0 + 2 πn, x + \frac{π}{4} = π + 2 πn

x + \frac{π}{4} = 0 + 2 πn, x + \frac{π}{4} = π + 2 πn

Solve

x + \frac{π}{4} = 0 + 2 πn : x = 2 πn - \frac{π}{4}

x + \frac{π}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

x + \frac{π}{4} = 2 πn

Move

\frac{π}{4}

to the right side

x + \frac{π}{4} = 2 πn

Subtract

\frac{π}{4}

from both sides

x + \frac{π}{4} - \frac{π}{4} = 2 πn - \frac{π}{4}

Simplify

x = 2 πn - \frac{π}{4}

x = 2 πn - \frac{π}{4}

Solve

x + \frac{π}{4} = π + 2 πn : x = π + 2 πn - \frac{π}{4}

x + \frac{π}{4} = π + 2 πn

Move

\frac{π}{4}

to the right side

x + \frac{π}{4} = π + 2 πn

Subtract

\frac{π}{4}

from both sides

x + \frac{π}{4} - \frac{π}{4} = π + 2 πn - \frac{π}{4}

Simplify

x = π + 2 πn - \frac{π}{4}

x = π + 2 πn - \frac{π}{4}

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

sin (x) = \frac{2 ( 5.5 \cdot 1 0 ^{- 7} )}{3.36 \cdot 1 0 ^{- 5}}

sin (x - 3 0^{\circ}) = cos (1 5^{\circ})

tan (x) = 2.8867

3 = cot (q)

sin (t) + cos (2 t) = 0

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