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

The general solution for ((sqrt(2))/2)(cos(θ)+sin(θ))=0 is θ=(3pi)/4+pin

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((sqrt(2))/2)(cos(θ)+sin(θ))=0

(\frac{2}{2}) (cos (θ) + sin (θ)) = 0

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

(\frac{2}{2}) (cos (θ) + sin (θ)) = 0

Rewrite using trig identities

\frac{2}{2} (cos (θ) + sin (θ)) = 0

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{\frac{2}{2} ( cos ( θ ) + sin ( θ ) )}{cos ( θ )} = \frac{0}{cos ( θ )}

Simplify

\frac{1}{2} + \frac{sin ( θ )}{2 cos ( θ )} = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

\frac{1 + tan ( θ )}{2} = 0

\frac{1 + tan ( θ )}{2} = 0

Multiply both sides by

2

\frac{1 + tan ( θ )}{2} = 0

Multiply both sides by

2

\frac{( 1 + tan ( θ ) ) 2}{2} = 0 \cdot 2

Simplify

1 + tan (θ) = 0

1 + tan (θ) = 0

Move

1

to the right side

1 + tan (θ) = 0

Subtract

1

from both sides

1 + tan (θ) - 1 = 0 - 1

Simplify

tan (θ) = - 1

tan (θ) = - 1

General solutions for

tan (θ) = - 1

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = \frac{3 π}{4} + πn

θ = \frac{3 π}{4} + πn

12 sin (x) - 2 = 2 + 8 sin (x)

cos (2 x + 30) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

tan (θ) = \frac{43}{90}

2 sin (2 x + \frac{π}{3}) = 1

sec (x) = 2, cos (x)

What is the general solution for ((sqrt(2))/2)(cos(θ)+sin(θ))=0 ?
The general solution for ((sqrt(2))/2)(cos(θ)+sin(θ))=0 is θ=(3pi)/4+pin