What is the general solution for sin(x)= 8/17 sin(2x) ?

The general solution for sin(x)= 8/17 sin(2x) is x=2pin,x=pi+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)= 8/17 sin(2x)

sin (x) = \frac{8}{17} sin (2 x)

x = 2 πn, x = π + 2 πn

Solution steps

sin (x) = \frac{8}{17} sin (2 x)

Subtract

\frac{8}{17} sin (2 x)

from both sides

sin (x) - \frac{8}{17} sin (2 x) = 0

Simplify

sin (x) - \frac{8}{17} sin (2 x) : \frac{17 sin ( x ) - 8 sin ( 2 x )}{17}

\frac{17 sin ( x ) - 8 sin ( 2 x )}{17} = 0

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

17 sin (x) - 8 sin (2 x) = 0

Rewrite using trig identities

17 sin (x) - 16 cos (x) sin (x) = 0

Factor

17 sin (x) - 16 cos (x) sin (x) : - sin (x) (16 cos (x) - 17)

- sin (x) (16 cos (x) - 17) = 0

Solving each part separately

sin (x) = 0 or 16 cos (x) - 17 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

16 cos (x) - 17 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

2 = 1 + sin (2 x)

cosh (x - 1) = 2

tan (x) = \frac{7}{25}

tan (x) = - 1, 0 < x < 2 π

sec^{2} (x) - 2 = tan^{2} (x), 0 \leq x \leq 2 π

What is the general solution for sin(x)= 8/17 sin(2x) ?
The general solution for sin(x)= 8/17 sin(2x) is x=2pin,x=pi+2pin