What is the general solution for sin(θ)+cos(θ)=-1 ?

The general solution for sin(θ)+cos(θ)=-1 is θ=2pin+pi,θ=2pin+(3pi)/2

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sin(θ)+cos(θ)=-1

sin (θ) + cos (θ) = - 1

θ = 2 πn + π, θ = 2 πn + \frac{3 π}{2}

Solution steps

sin (θ) + cos (θ) = - 1

Rewrite using trig identities

2 sin (θ + \frac{π}{4}) = - 1

Divide both sides by

2

sin (θ + \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (θ + \frac{π}{4}) = - \frac{2}{2}

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

Solve

θ + \frac{π}{4} = \frac{5 π}{4} + 2 πn : θ = 2 πn + π

Solve

θ + \frac{π}{4} = \frac{7 π}{4} + 2 πn : θ = 2 πn + \frac{3 π}{2}

θ = 2 πn + π, θ = 2 πn + \frac{3 π}{2}

6 sin (3 x) = 0

tan (x) = \frac{7}{24}

5 sin (x) = 2 cos^{2} (x) - 4

2 sin (x - \frac{π}{2}) + 2 = 0

tan (2 t) + tan (t) = 1 - tan (2 t) tan (t)

What is the general solution for sin(θ)+cos(θ)=-1 ?
The general solution for sin(θ)+cos(θ)=-1 is θ=2pin+pi,θ=2pin+(3pi)/2