What is the general solution for sin(x)=-cos(2x) ?

The general solution for sin(x)=-cos(2x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)=-cos(2x)

sin (x) = - cos (2 x)

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

sin (x) = - cos (2 x)

Subtract

- cos (2 x)

from both sides

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

Rewrite using trig identities

1 + sin (x) - 2 sin^{2} (x) = 0

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

csc (\frac{π}{24} x) = 1

cos (x) = \frac{6}{18}

4 cos (2 x) + 10 sin (x) - 7 = 0

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

2 sin (2 t) = 0

What is the general solution for sin(x)=-cos(2x) ?
The general solution for sin(x)=-cos(2x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin