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

The general solution for sin(x+1)=cos(x) is x=-2pin-1/2+pi/4 ,x=-1/2-(3pi)/4-2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x+1)=cos(x)

sin (x + 1) = cos (x)

x = - 2 πn - \frac{1}{2} + \frac{π}{4}, x = - \frac{1}{2} - \frac{3 π}{4} - 2 πn

Solution steps

sin (x + 1) = cos (x)

Subtract

cos (x)

from both sides

sin (x + 1) - cos (x) = 0

Rewrite using trig identities

- 2 sin (\frac{- 2 + π}{4}) sin (\frac{- 2 + π - 4 x}{4}) = 0

Divide both sides by

- 2 sin (\frac{- 2 + π}{4})

sin (\frac{- 2 + π - 4 x}{4}) = 0

General solutions for

sin (\frac{- 2 + π - 4 x}{4}) = 0

\frac{- 2 + π - 4 x}{4} = 0 + 2 πn, \frac{- 2 + π - 4 x}{4} = π + 2 πn

Solve

\frac{- 2 + π - 4 x}{4} = 0 + 2 πn : x = - 2 πn - \frac{1}{2} + \frac{π}{4}

Solve

\frac{- 2 + π - 4 x}{4} = π + 2 πn : x = - \frac{1}{2} - \frac{3 π}{4} - 2 πn

x = - 2 πn - \frac{1}{2} + \frac{π}{4}, x = - \frac{1}{2} - \frac{3 π}{4} - 2 πn

3 cos (x) - 2 = 1

sin (4 x) = - sin (2 x)

t, x = 1 - 2 cos (2 t)

x, sin (3 x) = - \frac{3}{2}

cos (x) = 0.587

What is the general solution for sin(x+1)=cos(x) ?
The general solution for sin(x+1)=cos(x) is x=-2pin-1/2+pi/4 ,x=-1/2-(3pi)/4-2pin