What is the general solution for csc(x-30)=2 ?

The general solution for csc(x-30)=2 is x=60+360n,x=360n+180

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csc(x-30)=2

Solution

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

Solution

x = 6 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} n + 18 0^{\circ}

Radians

x = \frac{π}{3} + 2 πn, x = π + 2 πn

Solution steps

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

General solutions for

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

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 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 = 6 0^{\circ} + 36 0^{\circ} n

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

Move

3 0^{\circ}

to the right side

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

Add

3 0^{\circ}

to both sides

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

Simplify

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

3 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ} : 6 0^{\circ} + 36 0^{\circ} n

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

Group like terms

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

Combine the fractions

3 0^{\circ} + 3 0^{\circ} : 6 0^{\circ}

Apply rule

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

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

Add similar elements:

18 0^{\circ} + 18 0^{\circ} = 36 0^{\circ}

= 6 0^{\circ}

Cancel the common factor:

2

= 6 0^{\circ}

= 6 0^{\circ} + 36 0^{\circ} n

x = 6 0^{\circ} + 36 0^{\circ} n

x = 6 0^{\circ} + 36 0^{\circ} n

x = 6 0^{\circ} + 36 0^{\circ} n

Solve

x - 3 0^{\circ} = 15 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 18 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

Add

3 0^{\circ}

to 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 + 18 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} : 18 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} = 108 0^{\circ}

= 18 0^{\circ}

Divide the numbers:

\frac{6}{6} = 1

= 18 0^{\circ}

= 36 0^{\circ} n + 18 0^{\circ}

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

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

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

x = 6 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} n + 18 0^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for csc(x-30)=2 ?
The general solution for csc(x-30)=2 is x=60+360n,x=360n+180