What is the general solution for cos(x+30)=0 ?

The general solution for cos(x+30)=0 is x=360n+60,x=360n+240

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

cos(x+30)=0

Solution

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

Solution

x = 36 0^{\circ} n + 6 0^{\circ}, x = 36 0^{\circ} n + 24 0^{\circ}

Radians

x = \frac{π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

General solutions for

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

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x + 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

x + 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

Solve

x + 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 6 0^{\circ}

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

Move

3 0^{\circ}

to the right side

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

Subtract

3 0^{\circ}

from both sides

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

Simplify

x + 3 0^{\circ} - 3 0^{\circ} = 9 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

9 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ} : 36 0^{\circ} n + 6 0^{\circ}

9 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

Group like terms

= 36 0^{\circ} n + 9 0^{\circ} - 3 0^{\circ}

Least Common Multiplier of

2, 6 : 6

2, 6

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Multiply each factor the greatest number of times it occurs in either

2

6

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

9 0^{\circ} :

multiply the denominator and numerator by

3

9 0^{\circ} = \frac{18 0 ^{\circ} 3}{2 \cdot 3} = 9 0^{\circ}

= 9 0^{\circ} - 3 0^{\circ}

Since the denominators are equal, combine the fractions:

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

= \frac{18 0 ^{\circ} 3 - 18 0 ^{\circ}}{6}

Add similar elements:

54 0^{\circ} - 18 0^{\circ} = 36 0^{\circ}

= 6 0^{\circ}

Cancel the common factor:

2

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

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

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

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

Solve

x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 24 0^{\circ}

x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

Subtract

3 0^{\circ}

from both sides

x + 3 0^{\circ} - 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

Simplify

x + 3 0^{\circ} - 3 0^{\circ} = 27 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

27 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ} : 36 0^{\circ} n + 24 0^{\circ}

27 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

Group like terms

= 36 0^{\circ} n - 3 0^{\circ} + 27 0^{\circ}

Least Common Multiplier of

6, 2 : 6

6, 2

Least Common Multiplier (LCM)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Multiply each factor the greatest number of times it occurs in either

6

2

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

27 0^{\circ} :

multiply the denominator and numerator by

3

27 0^{\circ} = \frac{54 0 ^{\circ} 3}{2 \cdot 3} = 27 0^{\circ}

= - 3 0^{\circ} + 27 0^{\circ}

Since the denominators are equal, combine the fractions:

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

= \frac{- 18 0 ^{\circ} + 162 0 ^{\circ}}{6}

Add similar elements:

- 18 0^{\circ} + 162 0^{\circ} = 144 0^{\circ}

= 24 0^{\circ}

Cancel the common factor:

2

= 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n + 24 0^{\circ}

x = 36 0^{\circ} n + 6 0^{\circ}, x = 36 0^{\circ} n + 24 0^{\circ}

Graph

Popular Examples

cos(2x)-sin^2(x)-1/4 =0

Frequently Asked Questions (FAQ)

What is the general solution for cos(x+30)=0 ?
The general solution for cos(x+30)=0 is x=360n+60,x=360n+240