What is the general solution for 2sin(2x-10)-sqrt(3)=0 ?

The general solution for 2sin(2x-10)-sqrt(3)=0 is x=5+pin+pi/6 ,x=5+pin+pi/3

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2sin(2x-10)-sqrt(3)=0

Solution

2 sin (2 x - 10) - 3 = 0

Solution

x = 5 + πn + \frac{π}{6}, x = 5 + πn + \frac{π}{3}

Degrees

x = 316.47889 \dots^{\circ} + 18 0^{\circ} n, x = 346.47889 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 sin (2 x - 10) - 3 = 0

Move

3

to the right side

2 sin (2 x - 10) - 3 = 0

Add

3

to both sides

2 sin (2 x - 10) - 3 + 3 = 0 + 3

Simplify

2 sin (2 x - 10) = 3

2 sin (2 x - 10) = 3

Divide both sides by

2

2 sin (2 x - 10) = 3

Divide both sides by

2

\frac{2 sin ( 2 x - 10 )}{2} = \frac{3}{2}

Simplify

sin (2 x - 10) = \frac{3}{2}

sin (2 x - 10) = \frac{3}{2}

General solutions for

sin (2 x - 10) = \frac{3}{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}

2 x - 10 = \frac{π}{3} + 2 πn, 2 x - 10 = \frac{2 π}{3} + 2 πn

2 x - 10 = \frac{π}{3} + 2 πn, 2 x - 10 = \frac{2 π}{3} + 2 πn

Solve

2 x - 10 = \frac{π}{3} + 2 πn : x = 5 + πn + \frac{π}{6}

2 x - 10 = \frac{π}{3} + 2 πn

Move

10

to the right side

2 x - 10 = \frac{π}{3} + 2 πn

Add

10

to both sides

2 x - 10 + 10 = \frac{π}{3} + 2 πn + 10

Simplify

2 x = \frac{π}{3} + 2 πn + 10

2 x = \frac{π}{3} + 2 πn + 10

Divide both sides by

2

2 x = \frac{π}{3} + 2 πn + 10

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} + \frac{10}{2} : 5 + πn + \frac{π}{6}

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} + \frac{10}{2}

Group like terms

= \frac{10}{2} + \frac{2 πn}{2} + \frac{\frac{π}{3}}{2}

\frac{10}{2} = 5

\frac{10}{2}

Divide the numbers:

\frac{10}{2} = 5

= 5

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= 5 + πn + \frac{π}{6}

x = 5 + πn + \frac{π}{6}

x = 5 + πn + \frac{π}{6}

x = 5 + πn + \frac{π}{6}

Solve

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

2 x - 10 = \frac{2 π}{3} + 2 πn

Move

10

to the right side

2 x - 10 = \frac{2 π}{3} + 2 πn

Add

10

to both sides

2 x - 10 + 10 = \frac{2 π}{3} + 2 πn + 10

Simplify

2 x = \frac{2 π}{3} + 2 πn + 10

2 x = \frac{2 π}{3} + 2 πn + 10

Divide both sides by

2

2 x = \frac{2 π}{3} + 2 πn + 10

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

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

\frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} + \frac{10}{2}

Group like terms

= \frac{10}{2} + \frac{2 πn}{2} + \frac{\frac{2 π}{3}}{2}

\frac{10}{2} = 5

\frac{10}{2}

Divide the numbers:

\frac{10}{2} = 5

= 5

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{2 π}{3}}{2} = \frac{π}{3}

\frac{\frac{2 π}{3}}{2}

Apply the fraction rule:

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

= \frac{2 π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{2 π}{6}

Cancel the common factor:

2

= \frac{π}{3}

= 5 + πn + \frac{π}{3}

x = 5 + πn + \frac{π}{3}

x = 5 + πn + \frac{π}{3}

x = 5 + πn + \frac{π}{3}

x = 5 + πn + \frac{π}{6}, x = 5 + πn + \frac{π}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 2sin(2x-10)-sqrt(3)=0 ?
The general solution for 2sin(2x-10)-sqrt(3)=0 is x=5+pin+pi/6 ,x=5+pin+pi/3