What is the general solution for sin(x/5)=(sqrt(2))/2 ?

The general solution for sin(x/5)=(sqrt(2))/2 is x=(5pi)/4+10pin,x=(15pi)/4+10pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x/5)=(sqrt(2))/2

Solution

sin (\frac{x}{5}) = \frac{2}{2}

Solution

x = \frac{5 π}{4} + 10 πn, x = \frac{15 π}{4} + 10 πn

Degrees

x = 22 5^{\circ} + 180 0^{\circ} n, x = 67 5^{\circ} + 180 0^{\circ} n

Solution steps

sin (\frac{x}{5}) = \frac{2}{2}

General solutions for

sin (\frac{x}{5}) = \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{x}{5} = \frac{π}{4} + 2 πn, \frac{x}{5} = \frac{3 π}{4} + 2 πn

\frac{x}{5} = \frac{π}{4} + 2 πn, \frac{x}{5} = \frac{3 π}{4} + 2 πn

Solve

\frac{x}{5} = \frac{π}{4} + 2 πn : x = \frac{5 π}{4} + 10 πn

\frac{x}{5} = \frac{π}{4} + 2 πn

Multiply both sides by

5

\frac{x}{5} = \frac{π}{4} + 2 πn

Multiply both sides by

5

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

Simplify

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

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

5 \cdot \frac{π}{4} + 5 \cdot 2 πn : \frac{5 π}{4} + 10 πn

5 \cdot \frac{π}{4} + 5 \cdot 2 πn

Multiply

5 \cdot \frac{π}{4} : \frac{5 π}{4}

5 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 5}{4}

= \frac{5 π}{4} + 5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= \frac{5 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn

Solve

\frac{x}{5} = \frac{3 π}{4} + 2 πn : x = \frac{15 π}{4} + 10 πn

\frac{x}{5} = \frac{3 π}{4} + 2 πn

Multiply both sides by

5

\frac{x}{5} = \frac{3 π}{4} + 2 πn

Multiply both sides by

5

\frac{5 x}{5} = 5 \cdot \frac{3 π}{4} + 5 \cdot 2 πn

Simplify

\frac{5 x}{5} = 5 \cdot \frac{3 π}{4} + 5 \cdot 2 πn

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

5 \cdot \frac{3 π}{4} + 5 \cdot 2 πn : \frac{15 π}{4} + 10 πn

5 \cdot \frac{3 π}{4} + 5 \cdot 2 πn

5 \cdot \frac{3 π}{4} = \frac{15 π}{4}

5 \cdot \frac{3 π}{4}

Multiply fractions:

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

= \frac{3 π 5}{4}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{15 π}{4}

5 \cdot 2 πn = 10 πn

5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= 10 πn

= \frac{15 π}{4} + 10 πn

x = \frac{15 π}{4} + 10 πn

x = \frac{15 π}{4} + 10 πn

x = \frac{15 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn, x = \frac{15 π}{4} + 10 πn

Popular Examples

solvefor x,sin(x)=0.6 solve for

x, sin (x) = 0.6

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

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

tan^2(θ)+2tan(θ)=-1

tan^{2} (θ) + 2 tan (θ) = - 1

cos(a)= 2/3

cos (a) = \frac{2}{3}

-1=cos(pit)

- 1 = cos (π t)

Frequently Asked Questions (FAQ)

What is the general solution for sin(x/5)=(sqrt(2))/2 ?
The general solution for sin(x/5)=(sqrt(2))/2 is x=(5pi)/4+10pin,x=(15pi)/4+10pin