What is the general solution for sin(x/7)=(3^{1/2})/2 ,pi<x<3pi ?

Q: What is the general solution for sin(x/7)=(3^{1/2})/2 ,pi<x<3pi ?

The general solution for sin(x/7)=(3^{1/2})/2 ,pi<x<3pi is x=(7pi)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

sin(x/7)=(3^{1/2})/2 ,pi<x<3pi

Solution

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}, π < x < 3 π

Solution

x = \frac{7 π}{3}

Degrees

x = 42 0^{\circ}

Solution steps

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}, π < x < 3 π

Apply trig inverse properties

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}

General solutions for

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}

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

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn, \frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn, \frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Solve

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : x = \frac{7 π}{3} + 14 πn

\frac{x}{7} = arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Simplify

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : \frac{π}{3} + 2 πn

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Use the following trivial identity:

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) = \frac{π}{3}

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{3} + 2 πn

\frac{x}{7} = \frac{π}{3} + 2 πn

Multiply both sides by

7

\frac{x}{7} = \frac{π}{3} + 2 πn

Multiply both sides by

7

\frac{7 x}{7} = 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplify

\frac{7 x}{7} = 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplify

\frac{7 x}{7} : x

\frac{7 x}{7}

Divide the numbers:

\frac{7}{7} = 1

= x

Simplify

7 \cdot \frac{π}{3} + 7 \cdot 2 πn : \frac{7 π}{3} + 14 πn

7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Multiply

7 \cdot \frac{π}{3} : \frac{7 π}{3}

7 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 7}{3}

= \frac{7 π}{3} + 7 \cdot 2 πn

Multiply the numbers:

7 \cdot 2 = 14

= \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn

Solve

\frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : x = 7 π - \frac{7 π}{3} + 14 πn

\frac{x}{7} = π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Simplify

π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn : π - \frac{π}{3} + 2 πn

π - arcsin (\frac{3 ^{\frac{1}{2}}}{2}) + 2 πn

Use the following trivial identity:

arcsin (\frac{3 ^{\frac{1}{2}}}{2}) = \frac{π}{3}

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= π - \frac{π}{3} + 2 πn

\frac{x}{7} = π - \frac{π}{3} + 2 πn

Multiply both sides by

7

\frac{x}{7} = π - \frac{π}{3} + 2 πn

Multiply both sides by

7

\frac{7 x}{7} = 7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplify

\frac{7 x}{7} = 7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Simplify

\frac{7 x}{7} : x

\frac{7 x}{7}

Divide the numbers:

\frac{7}{7} = 1

= x

Simplify

7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn : 7 π - \frac{7 π}{3} + 14 πn

7 π - 7 \cdot \frac{π}{3} + 7 \cdot 2 πn

Multiply

7 \cdot \frac{π}{3} : \frac{7 π}{3}

7 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 7}{3}

= 7 π - \frac{7 π}{3} + 7 \cdot 2 πn

Multiply the numbers:

7 \cdot 2 = 14

= 7 π - \frac{7 π}{3} + 14 πn

x = 7 π - \frac{7 π}{3} + 14 πn

x = 7 π - \frac{7 π}{3} + 14 πn

x = 7 π - \frac{7 π}{3} + 14 πn

x = \frac{7 π}{3} + 14 πn, x = 7 π - \frac{7 π}{3} + 14 πn

Solutions for the range

π < x < 3 π

x = \frac{7 π}{3}

Graph

Popular Examples

2sec^2(x)-13sec(x)+20=0,2pi<= x<= 4pi

Frequently Asked Questions (FAQ)

What is the general solution for sin(x/7)=(3^{1/2})/2 ,pi<x<3pi ?
The general solution for sin(x/7)=(3^{1/2})/2 ,pi<x<3pi is x=(7pi)/3