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

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

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sin(x)+cos(x)=-1

sin (x) + cos (x) = - 1

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

Solution steps

sin (x) + cos (x) = - 1

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = - 1

Divide both sides by

2

sin (x + \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = - \frac{2}{2}

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

Solve

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

Solve

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

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

3 sec (x) + 2 = 0

sin (x) + cos (x) = 3

sin^{2} (θ) = \frac{3}{4}

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

- sin (x) + cos (2 x) = 1

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