What is the general solution for tan(x)+4sin(x)=0 ?

The general solution for tan(x)+4sin(x)=0 is x=2pin,x=pi+2pin,x=1.82347…+2pin,x=-1.82347…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x)+4sin(x)=0

tan (x) + 4 sin (x) = 0

x = 2 πn, x = π + 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

Solution steps

tan (x) + 4 sin (x) = 0

Express with sin, cos

\frac{sin ( x ) + 4 cos ( x ) sin ( x )}{cos ( x )} = 0

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

sin (x) + 4 cos (x) sin (x) = 0

Factor

sin (x) + 4 cos (x) sin (x) : sin (x) (4 cos (x) + 1)

sin (x) (4 cos (x) + 1) = 0

Solving each part separately

sin (x) = 0 or 4 cos (x) + 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

4 cos (x) + 1 = 0 : x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

1 + 2 \cdot sin (x) = 2

1 + 2 \cdot sin (x) = 3

sin (α) = \frac{120 sin ( 6 0 ^{\circ} )}{1200}

15.8 \cdot sin (30 x - 90) + 5 = 17

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

What is the general solution for tan(x)+4sin(x)=0 ?
The general solution for tan(x)+4sin(x)=0 is x=2pin,x=pi+2pin,x=1.82347…+2pin,x=-1.82347…+2pin