What is the general solution for 8sin(x)tan(x)+tan(x)=0 ?

The general solution for 8sin(x)tan(x)+tan(x)=0 is x=pin,x=-0.12532…+2pin,x=pi+0.12532…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8sin(x)tan(x)+tan(x)=0

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

x = πn, x = - 0.12532 \dots + 2 πn, x = π + 0.12532 \dots + 2 πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n, x = - 7.18075 \dots^{\circ} + 36 0^{\circ} n, x = 187.18075 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Factor

8 sin (x) tan (x) + tan (x) : tan (x) (8 sin (x) + 1)

8 sin (x) tan (x) + tan (x)

Factor out common term

tan (x)

= tan (x) (8 sin (x) + 1)

tan (x) (8 sin (x) + 1) = 0

Solving each part separately

tan (x) = 0 or 8 sin (x) + 1 = 0

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

8 sin (x) + 1 = 0 : x = arcsin (- \frac{1}{8}) + 2 πn, x = π + arcsin (\frac{1}{8}) + 2 πn

8 sin (x) + 1 = 0

Move

1

to the right side

8 sin (x) + 1 = 0

Subtract

1

from both sides

8 sin (x) + 1 - 1 = 0 - 1

Simplify

8 sin (x) = - 1

8 sin (x) = - 1

Divide both sides by

8

8 sin (x) = - 1

Divide both sides by

8

\frac{8 sin ( x )}{8} = \frac{- 1}{8}

Simplify

sin (x) = - \frac{1}{8}

sin (x) = - \frac{1}{8}

Apply trig inverse properties

sin (x) = - \frac{1}{8}

General solutions for

sin (x) = - \frac{1}{8}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{1}{8}) + 2 πn, x = π + arcsin (\frac{1}{8}) + 2 πn

x = arcsin (- \frac{1}{8}) + 2 πn, x = π + arcsin (\frac{1}{8}) + 2 πn

Combine all the solutions

x = πn, x = arcsin (- \frac{1}{8}) + 2 πn, x = π + arcsin (\frac{1}{8}) + 2 πn

Show solutions in decimal form

x = πn, x = - 0.12532 \dots + 2 πn, x = π + 0.12532 \dots + 2 πn

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

sin (x) + 4 csc (x) + 5 = 0

sin (x) = \frac{5}{9}

sin (x) = \frac{5}{3}

tan (3 x) = \frac{1}{3}

What is the general solution for 8sin(x)tan(x)+tan(x)=0 ?
The general solution for 8sin(x)tan(x)+tan(x)=0 is x=pin,x=-0.12532…+2pin,x=pi+0.12532…+2pin