What is the general solution for 1= 1/(0.5)sin(x+30) ?

The general solution for 1= 1/(0.5)sin(x+30) is x=360n,x=360n+120

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Popular Trigonometry >

1= 1/(0.5)sin(x+30)

Solution

1 = \frac{1}{0.5} sin (x + 3 0^{\circ})

Solution

x = 36 0^{\circ} n, x = 36 0^{\circ} n + 12 0^{\circ}

Radians

x = 0 + 2 πn, x = \frac{2 π}{3} + 2 πn

Solution steps

1 = \frac{1}{0.5} sin (x + 3 0^{\circ})

Switch sides

\frac{1}{0.5} sin (x + 3 0^{\circ}) = 1

Multiply both sides by

0.5

\frac{1}{0.5} sin (x + 3 0^{\circ}) = 1

Multiply both sides by

0.5

0.5 \cdot \frac{1}{0.5} sin (x + 3 0^{\circ}) = 1 \cdot 0.5

Simplify

sin (x + 3 0^{\circ}) = 0.5

sin (x + 3 0^{\circ}) = 0.5

General solutions for

sin (x + 3 0^{\circ}) = 0.5

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}

x + 3 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n, x + 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n

x + 3 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n, x + 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n

Solve

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

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

Subtract

3 0^{\circ}

from both sides

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

Simplify

x = 36 0^{\circ} n

Solve

x + 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 12 0^{\circ}

x + 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x + 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n

Subtract

3 0^{\circ}

from both sides

x + 3 0^{\circ} - 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

Simplify

x + 3 0^{\circ} - 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

Simplify

x + 3 0^{\circ} - 3 0^{\circ} : x

x + 3 0^{\circ} - 3 0^{\circ}

Add similar elements:

3 0^{\circ} - 3 0^{\circ} = 0

= x

Simplify

15 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ} : 36 0^{\circ} n + 12 0^{\circ}

15 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

Group like terms

= 36 0^{\circ} n - 3 0^{\circ} + 15 0^{\circ}

Combine the fractions

- 3 0^{\circ} + 15 0^{\circ} : 12 0^{\circ}

Apply rule

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

= \frac{- 18 0 ^{\circ} + 90 0 ^{\circ}}{6}

Add similar elements:

- 18 0^{\circ} + 90 0^{\circ} = 72 0^{\circ}

= 12 0^{\circ}

Cancel the common factor:

2

= 12 0^{\circ}

= 36 0^{\circ} n + 12 0^{\circ}

x = 36 0^{\circ} n + 12 0^{\circ}

x = 36 0^{\circ} n + 12 0^{\circ}

x = 36 0^{\circ} n + 12 0^{\circ}

x = 36 0^{\circ} n, x = 36 0^{\circ} n + 12 0^{\circ}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 1= 1/(0.5)sin(x+30) ?
The general solution for 1= 1/(0.5)sin(x+30) is x=360n,x=360n+120