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+pi/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{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{π}{2} + 2 πn

Solve

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

θ = 2 πn + \frac{π}{4}

sin^{2} (x) - cos^{2} (x) = \frac{1}{2}

2 sin^{2} (x) + cos (x) = 0

sec (3 x) = \frac{2}{3}, 0 \leq x \leq 2 π

sec (4 x) - 2 = 0

2 cos (θ) sin (θ) = cos (θ)

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+pi/4