What is the general solution for cos(2x+30)=0 ?

The general solution for cos(2x+30)=0 is x=180n+30,x=180n+120

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(2x+30)=0

Solution

cos (2 x + 3 0^{\circ}) = 0

Solution

x = 18 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} n + 12 0^{\circ}

Radians

x = \frac{π}{6} + πn, x = \frac{2 π}{3} + πn

Solution steps

cos (2 x + 3 0^{\circ}) = 0

General solutions for

cos (2 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}

2 x + 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, 2 x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

2 x + 3 0^{\circ} = 9 0^{\circ} + 36 0^{\circ} n, 2 x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n

Solve

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

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

Move

3 0^{\circ}

to the right side

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

Subtract

3 0^{\circ}

from both sides

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

Simplify

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

Simplify

2 x + 3 0^{\circ} - 3 0^{\circ} : 2 x

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

Add similar elements:

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

= 2 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}

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

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

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

Divide both sides by

2

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

Divide both sides by

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{6 0 ^{\circ}}{2}

Simplify

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{6 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{6 0 ^{\circ}}{2} : 18 0^{\circ} n + 3 0^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{6 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{6 0 ^{\circ}}{2} = 3 0^{\circ}

\frac{6 0 ^{\circ}}{2}

Apply the fraction rule:

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

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

Multiply the numbers:

3 \cdot 2 = 6

= 3 0^{\circ}

= 18 0^{\circ} n + 3 0^{\circ}

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

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

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

Solve

2 x + 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 12 0^{\circ}

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

Move

3 0^{\circ}

to the right side

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

Subtract

3 0^{\circ}

from both sides

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

Simplify

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

Simplify

2 x + 3 0^{\circ} - 3 0^{\circ} : 2 x

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

Add similar elements:

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

= 2 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}

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

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

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

Divide both sides by

2

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

Divide both sides by

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{24 0 ^{\circ}}{2}

Simplify

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{24 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{24 0 ^{\circ}}{2} : 18 0^{\circ} n + 12 0^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{24 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{24 0 ^{\circ}}{2} = 12 0^{\circ}

\frac{24 0 ^{\circ}}{2}

Apply the fraction rule:

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

= \frac{72 0 ^{\circ}}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= 12 0^{\circ}

Cancel the common factor:

2

= 12 0^{\circ}

= 18 0^{\circ} n + 12 0^{\circ}

x = 18 0^{\circ} n + 12 0^{\circ}

x = 18 0^{\circ} n + 12 0^{\circ}

x = 18 0^{\circ} n + 12 0^{\circ}

x = 18 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} n + 12 0^{\circ}

Popular Examples

cos(x)-2cos(x)*sin(x)=0

cos (x) - 2 cos (x) \cdot sin (x) = 0

sin(θ)=0.695

sin (θ) = 0.695

4+sin(a)=3sin^2(a)

4 + sin (a) = 3 sin^{2} (a)

solvefor x,cos(2x)-cos(x)=0 solve for

x, cos (2 x) - cos (x) = 0

tan^2(x)+2tan(x)-1=0

tan^{2} (x) + 2 tan (x) - 1 = 0

Frequently Asked Questions (FAQ)

What is the general solution for cos(2x+30)=0 ?
The general solution for cos(2x+30)=0 is x=180n+30,x=180n+120