What is the general solution for sin(2x-pi/6)=0,0<= x<= 360 ?

Q: What is the general solution for sin(2x-pi/6)=0,0<= x<= 360 ?

The general solution for sin(2x-pi/6)=0,0<= x<= 360 is x=15,x=105,x=195,x=285

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sin(2x-pi/6)=0,0<= x<= 360

Solution

sin (2 x - \frac{π}{6}) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

Solution

x = 1 5^{\circ}, x = 10 5^{\circ}, x = 19 5^{\circ}, x = 28 5^{\circ}

Radians

x = \frac{π}{12}, x = \frac{7 π}{12}, x = \frac{13 π}{12}, x = \frac{19 π}{12}

Solution steps

sin (2 x - \frac{π}{6}) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

General solutions for

sin (2 x - 3 0^{\circ}) = 0

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 x - 3 0^{\circ} = 0 + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

2 x - 3 0^{\circ} = 0 + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

Solve

2 x - 3 0^{\circ} = 0 + 36 0^{\circ} n : x = 18 0^{\circ} n + 1 5^{\circ}

2 x - 3 0^{\circ} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

2 x - 3 0^{\circ} = 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

2 x - 3 0^{\circ} = 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

2 x - 3 0^{\circ} + 3 0^{\circ} = 36 0^{\circ} n + 3 0^{\circ}

Simplify

2 x = 36 0^{\circ} n + 3 0^{\circ}

2 x = 36 0^{\circ} n + 3 0^{\circ}

Divide both sides by

2

2 x = 36 0^{\circ} n + 3 0^{\circ}

Divide both sides by

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplify

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} : 18 0^{\circ} n + 1 5^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Divide the numbers:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

Apply the fraction rule:

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

= \frac{18 0 ^{\circ}}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= 1 5^{\circ}

= 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}

Solve

2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

2 x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

Simplify

2 x = 18 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

2 x = 18 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

Divide both sides by

2

2 x = 18 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

Divide both sides by

2

\frac{2 x}{2} = 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplify

\frac{2 x}{2} = 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} : 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Divide the numbers:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

Apply the fraction rule:

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

= \frac{18 0 ^{\circ}}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= 1 5^{\circ}

= 9 0^{\circ} + 18 0^{\circ} n + 1 5^{\circ}

Group like terms

= 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

Solutions for the range

0 \leq x \leq 36 0^{\circ}

x = 1 5^{\circ}, x = 10 5^{\circ}, x = 19 5^{\circ}, x = 28 5^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for sin(2x-pi/6)=0,0<= x<= 360 ?
The general solution for sin(2x-pi/6)=0,0<= x<= 360 is x=15,x=105,x=195,x=285