What is the general solution for 2sin(4x)-sqrt(2)=0 ?

The general solution for 2sin(4x)-sqrt(2)=0 is x= pi/(16)+(pin)/2 ,x=(3pi}{16}+\frac{pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

2 sin (4 x) - 2 = 0

Solution

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

Degrees

x = 11.2 5^{\circ} + 9 0^{\circ} n, x = 33.7 5^{\circ} + 9 0^{\circ} n

Solution steps

2 sin (4 x) - 2 = 0

Move

2

to the right side

2 sin (4 x) - 2 = 0

Add

2

to both sides

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

Simplify

2 sin (4 x) = 2

2 sin (4 x) = 2

Divide both sides by

2

2 sin (4 x) = 2

Divide both sides by

2

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

Simplify

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

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

General solutions for

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

sin (x)

periodicity table with

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

4 x = \frac{π}{4} + 2 πn, 4 x = \frac{3 π}{4} + 2 πn

4 x = \frac{π}{4} + 2 πn, 4 x = \frac{3 π}{4} + 2 πn

Solve

4 x = \frac{π}{4} + 2 πn : x = \frac{π}{16} + \frac{πn}{2}

4 x = \frac{π}{4} + 2 πn

Divide both sides by

4

4 x = \frac{π}{4} + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{π}{4}}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{π}{4}}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{π}{4}}{4} + \frac{2 πn}{4} : \frac{π}{16} + \frac{πn}{2}

\frac{\frac{π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{4}}{4} = \frac{π}{16}

\frac{\frac{π}{4}}{4}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 4}

Multiply the numbers:

4 \cdot 4 = 16

= \frac{π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}

Solve

4 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{16} + \frac{πn}{2}

4 x = \frac{3 π}{4} + 2 πn

Divide both sides by

4

4 x = \frac{3 π}{4} + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4} : \frac{3 π}{16} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{4} + \frac{2 πn}{4}

\frac{\frac{3 π}{4}}{4} = \frac{3 π}{16}

\frac{\frac{3 π}{4}}{4}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{4 \cdot 4}

Multiply the numbers:

4 \cdot 4 = 16

= \frac{3 π}{16}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

Popular Examples

6tan(x)sin(x)=7sin(x)

6 tan (x) sin (x) = 7 sin (x)

cos(2x)+cos(x)+1=0

cos (2 x) + cos (x) + 1 = 0

3tan^4(x)-10tan^2(x)+3=0

3 tan^{4} (x) - 10 tan^{2} (x) + 3 = 0

9sec(x)csc(x)=18csc(x)

9 sec (x) csc (x) = 18 csc (x)

2sin^2(x)=2-cos(x)

2 sin^{2} (x) = 2 - cos (x)

Frequently Asked Questions (FAQ)

What is the general solution for 2sin(4x)-sqrt(2)=0 ?
The general solution for 2sin(4x)-sqrt(2)=0 is x= pi/(16)+(pin)/2 ,x=(3pi}{16}+\frac{pin)/2