What is the general solution for 2sin(1/2 x)+sqrt(2)=0 ?

The general solution for 2sin(1/2 x)+sqrt(2)=0 is x=(5pi)/2+4pin,x=(7pi)/2+4pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(1/2 x)+sqrt(2)=0

Solution

2 sin (\frac{1}{2} x) + 2 = 0

Solution

x = \frac{5 π}{2} + 4 πn, x = \frac{7 π}{2} + 4 πn

Degrees

x = 45 0^{\circ} + 72 0^{\circ} n, x = 63 0^{\circ} + 72 0^{\circ} n

Solution steps

2 sin (\frac{1}{2} x) + 2 = 0

Move

2

to the right side

2 sin (\frac{1}{2} x) + 2 = 0

Subtract

2

from both sides

2 sin (\frac{1}{2} x) + 2 - 2 = 0 - 2

Simplify

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

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

General solutions for

sin (\frac{1}{2} 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}

\frac{1}{2} x = \frac{5 π}{4} + 2 πn, \frac{1}{2} x = \frac{7 π}{4} + 2 πn

\frac{1}{2} x = \frac{5 π}{4} + 2 πn, \frac{1}{2} x = \frac{7 π}{4} + 2 πn

Solve

\frac{1}{2} x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{2} + 4 πn

\frac{1}{2} x = \frac{5 π}{4} + 2 πn

Multiply both sides by

2

\frac{1}{2} x = \frac{5 π}{4} + 2 πn

Multiply both sides by

2

2 \cdot \frac{1}{2} x = 2 \cdot \frac{5 π}{4} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{1}{2} x = 2 \cdot \frac{5 π}{4} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiply fractions:

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

= \frac{1 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 1

Multiply:

x \cdot 1 = x

= x

Simplify

2 \cdot \frac{5 π}{4} + 2 \cdot 2 πn : \frac{5 π}{2} + 4 πn

2 \cdot \frac{5 π}{4} + 2 \cdot 2 πn

2 \cdot \frac{5 π}{4} = \frac{5 π}{2}

2 \cdot \frac{5 π}{4}

Multiply fractions:

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

= \frac{5 π 2}{4}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 π}{4}

Cancel the common factor:

2

= \frac{5 π}{2}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= \frac{5 π}{2} + 4 πn

x = \frac{5 π}{2} + 4 πn

x = \frac{5 π}{2} + 4 πn

x = \frac{5 π}{2} + 4 πn

Solve

\frac{1}{2} x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{2} + 4 πn

\frac{1}{2} x = \frac{7 π}{4} + 2 πn

Multiply both sides by

2

\frac{1}{2} x = \frac{7 π}{4} + 2 πn

Multiply both sides by

2

2 \cdot \frac{1}{2} x = 2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{1}{2} x = 2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiply fractions:

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

= \frac{1 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 1

Multiply:

x \cdot 1 = x

= x

Simplify

2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn : \frac{7 π}{2} + 4 πn

2 \cdot \frac{7 π}{4} + 2 \cdot 2 πn

2 \cdot \frac{7 π}{4} = \frac{7 π}{2}

2 \cdot \frac{7 π}{4}

Multiply fractions:

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

= \frac{7 π 2}{4}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{14 π}{4}

Cancel the common factor:

2

= \frac{7 π}{2}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= \frac{7 π}{2} + 4 πn

x = \frac{7 π}{2} + 4 πn

x = \frac{7 π}{2} + 4 πn

x = \frac{7 π}{2} + 4 πn

x = \frac{5 π}{2} + 4 πn, x = \frac{7 π}{2} + 4 πn

Popular Examples

(cos(x))/(sin(x))=-0.05467

\frac{cos ( x )}{sin ( x )} = - 0.05467

2sin^4(x)+2sin^2(x)cos^2(x)=1

2 sin^{4} (x) + 2 sin^{2} (x) cos^{2} (x) = 1

(1+4cos(θ))^2=(sqrt(3)sin(θ))^2

(1 + 4 cos (θ))^{2} = (3 sin (θ))^{2}

1/(tan(x))=4

\frac{1}{tan ( x )} = 4

sin^2(x)+2-3sin(x)=cos^2(x)

sin^{2} (x) + 2 - 3 sin (x) = cos^{2} (x)

Frequently Asked Questions (FAQ)

What is the general solution for 2sin(1/2 x)+sqrt(2)=0 ?
The general solution for 2sin(1/2 x)+sqrt(2)=0 is x=(5pi)/2+4pin,x=(7pi)/2+4pin