What is the general solution for sin(7x)+sin(x)=0,0<= x<= 2pi ?

The general solution for sin(7x)+sin(x)=0,0<= x<= 2pi is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(7x)+sin(x)=0,0<= x<= 2pi

sin (7 x) + sin (x) = 0, 0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{π}{2}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{3 π}{2}, x = \frac{11 π}{6}, x = 0, x = \frac{π}{4}, x = \frac{3 π}{4}, x = π, x = \frac{5 π}{4}, x = \frac{7 π}{4}, x = 2 π

Solution steps

sin (7 x) + sin (x) = 0, 0 \leq x \leq 2 π

Rewrite using trig identities

2 cos (3 x) sin (4 x) = 0

Solving each part separately

cos (3 x) = 0 or sin (4 x) = 0

cos (3 x) = 0, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{π}{2}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{3 π}{2}, x = \frac{11 π}{6}

sin (4 x) = 0, 0 \leq x \leq 2 π : x = 0, x = \frac{π}{4}, x = \frac{π}{2}, x = \frac{3 π}{4}, x = π, x = \frac{5 π}{4}, x = \frac{3 π}{2}, x = \frac{7 π}{4}, x = 2 π

Combine all the solutions

x = \frac{π}{6}, x = \frac{π}{2}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{3 π}{2}, x = \frac{11 π}{6}, x = 0, x = \frac{π}{4}, x = \frac{3 π}{4}, x = π, x = \frac{5 π}{4}, x = \frac{7 π}{4}, x = 2 π

t, - 2 sin (t) + 2 cos (2 t) = 0

2 cos (x) - 3 sin (x) = 1

cos^{2} (x) = tan (x)

sin^{2} (x) - 6 sin (x) + 3 = 0

12 csc^{2} (θ) - csc (θ) - 1 = 0

What is the general solution for sin(7x)+sin(x)=0,0<= x<= 2pi ?
The general solution for sin(7x)+sin(x)=0,0<= x<= 2pi is