What is the general solution for sin(2pix)cos(pix)+cos(2pix)sin(pix)=-1 ?

The general solution for sin(2pix)cos(pix)+cos(2pix)sin(pix)=-1 is x= 1/2+(2n)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2pix)cos(pix)+cos(2pix)sin(pix)=-1

sin (2 π x) cos (π x) + cos (2 π x) sin (π x) = - 1

x = \frac{1}{2} + \frac{2 n}{3}

Solution steps

sin (2 π x) cos (π x) + cos (2 π x) sin (π x) = - 1

Rewrite using trig identities

sin (2 π x + π x) = - 1

General solutions for

sin (2 π x + π x) = - 1

2 π x + π x = \frac{3 π}{2} + 2 πn

Solve

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

x = \frac{1}{2} + \frac{2 n}{3}

0 = - (sin (6.9256 - x) + (sin (- x)))

- 4 π^{2} sin (2 π x) = 0

- 9 sin (y) = 0

6 + 4 cos (2 x) = 2 - 4 cos (x)

x, cos (x) = y

What is the general solution for sin(2pix)cos(pix)+cos(2pix)sin(pix)=-1 ?
The general solution for sin(2pix)cos(pix)+cos(2pix)sin(pix)=-1 is x= 1/2+(2n)/3