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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(θ)+1=cos(θ)

sin (θ) + 1 = cos (θ)

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

Solution steps

sin (θ) + 1 = cos (θ)

Subtract

cos (θ)

from both sides

sin (θ) + 1 - cos (θ) = 0

Rewrite using trig identities

1 + 2 sin (θ - \frac{π}{4}) = 0

Move

1

to the right side

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 + \frac{3 π}{2}

Solve

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

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

2 sin^{2} (θ) - sin (θ) = 0

2 sin^{2} (x) = 2 - 3 cos (x)

tan^{2} (x) = \frac{3}{2} sec (x)

cot (θ) = cot^{2} (θ)

17 sin (x) + 8 = sin (x)

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