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

The general solution for sin(θ)+cos(θ)=-sqrt(2) is θ=2pin+(5pi)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(θ)+cos(θ)=-sqrt(2)

sin (θ) + cos (θ) = - 2

θ = 2 πn + \frac{5 π}{4}

Solution steps

sin (θ) + cos (θ) = - 2

Rewrite using trig identities

2 sin (θ + \frac{π}{4}) = - 2

Divide both sides by

2

sin (θ + \frac{π}{4}) = - 1

General solutions for

sin (θ + \frac{π}{4}) = - 1

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

Solve

θ + \frac{π}{4} = \frac{3 π}{2} + 2 πn : θ = 2 πn + \frac{5 π}{4}

θ = 2 πn + \frac{5 π}{4}

cot (2 x) = 1.732, 0 \leq x \leq 2 π

cot (θ) = 3.2404

8 sin^{2} (x) = 4

2 + 2 cos (2 x) = 0

cot (θ) = - 0.9

What is the general solution for sin(θ)+cos(θ)=-sqrt(2) ?
The general solution for sin(θ)+cos(θ)=-sqrt(2) is θ=2pin+(5pi)/4