What is the general solution for cos(x)=sin(x-pi/3) ?

The general solution for cos(x)=sin(x-pi/3) is x=1.30899…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)=sin(x-pi/3)

cos (x) = sin (x - \frac{π}{3})

x = 1.30899 \dots + πn

Solution steps

cos (x) = sin (x - \frac{π}{3})

Rewrite using trig identities

cos (x) = \frac{1}{2} sin (x) - \frac{3}{2} cos (x)

Subtract

\frac{1}{2} sin (x) - \frac{3}{2} cos (x)

from both sides

- \frac{1}{2} sin (x) + \frac{3 + 2}{2} cos (x) = 0

Simplify

- \frac{1}{2} sin (x) + \frac{3 + 2}{2} cos (x) : \frac{- sin ( x ) + ( 3 + 2 ) cos ( x )}{2}

\frac{- sin ( x ) + ( 3 + 2 ) cos ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- sin (x) + (3 + 2) cos (x) = 0

Rewrite using trig identities

- tan (x) + 3 + 2 = 0

Move

3

to the right side

- tan (x) + 2 = - 3

Move

2

to the right side

- tan (x) = - 3 - 2

Divide both sides by

- 1

tan (x) = 2 + 3

Apply trig inverse properties

x = arctan (2 + 3) + πn

Show solutions in decimal form

x = 1.30899 \dots + πn

sin (x + \frac{π}{4}) + sin (x + \frac{π}{4}) = - 1

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

4 sin^{2} (x) + 9 = 12

tan (- 60 s) = - tan (6 0^{\circ})

3 cos^{2} (x) - 5 cos (x) - 2 = 0, (0^{\circ}, 36 0^{\circ})

What is the general solution for cos(x)=sin(x-pi/3) ?
The general solution for cos(x)=sin(x-pi/3) is x=1.30899…+pin