en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

4sin(2x)tan(x)-tan(x)=0

Solution

4 sin (2 x) tan (x) - tan (x) = 0

Solution

x = πn, x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

+1

Degrees

x = 0^{\circ} + 18 0^{\circ} n, x = 7.23875 \dots^{\circ} + 18 0^{\circ} n, x = 82.76124 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 sin (2 x) tan (x) - tan (x) = 0

Factor

4 sin (2 x) tan (x) - tan (x) : tan (x) (4 sin (2 x) - 1)

4 sin (2 x) tan (x) - tan (x)

Factor out common term

tan (x)

= tan (x) (4 sin (2 x) - 1)

tan (x) (4 sin (2 x) - 1) = 0

Solving each part separately

tan (x) = 0 or 4 sin (2 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

4 sin (2 x) - 1 = 0 : x = \frac{arcsin ( \frac{1}{4} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

4 sin (2 x) - 1 = 0

Move

1

to the right side

4 sin (2 x) - 1 = 0

Add

1

to both sides

4 sin (2 x) - 1 + 1 = 0 + 1

Simplify

4 sin (2 x) = 1

4 sin (2 x) = 1

Divide both sides by

4

4 sin (2 x) = 1

Divide both sides by

4

\frac{4 sin ( 2 x )}{4} = \frac{1}{4}

Simplify

sin (2 x) = \frac{1}{4}

sin (2 x) = \frac{1}{4}

Apply trig inverse properties

sin (2 x) = \frac{1}{4}

General solutions for

sin (2 x) = \frac{1}{4}

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

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

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

Solve

2 x = arcsin (\frac{1}{4}) + 2 πn : x = \frac{arcsin ( \frac{1}{4} )}{2} + πn

2 x = arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{1}{4} )}{2} + πn

x = \frac{arcsin ( \frac{1}{4} )}{2} + πn

Solve

2 x = π - arcsin (\frac{1}{4}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

2 x = π - arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{1}{4}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

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

Combine all the solutions

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

Show solutions in decimal form

x = πn, x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

Graph

Popular Examples

3sin(x)=sqrt(3)*sin(x)+3cos(x)+3sin(x)

csc(θ)+1=0,(0,2pi)

solvefor x,y^2=-2tan(2x)

2cos^2(a)-3cos(a)+1=0

sin(x)*cos(2x)=0.5-sin(2x)*cos(x)