What is the general solution for solvefor x,1+sin(2x-30)=0 ?

The general solution for solvefor x,1+sin(2x-30)=0 is x=180n+150

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solvefor x,1+sin(2x-30)=0

Solution

solve for

x, 1 + sin (2 x - 3 0^{\circ}) = 0

Solution

x = 18 0^{\circ} n + 15 0^{\circ}

Radians

x = \frac{5 π}{6} + πn

Solution steps

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

Move

1

to the right side

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

Subtract

1

from both sides

1 + sin (2 x - 3 0^{\circ}) - 1 = 0 - 1

Simplify

sin (2 x - 3 0^{\circ}) = - 1

sin (2 x - 3 0^{\circ}) = - 1

General solutions for

sin (2 x - 3 0^{\circ}) = - 1

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

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

Solve

2 x - 3 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 15 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

Add

3 0^{\circ}

to 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 + 30 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} = 180 0^{\circ}

= 30 0^{\circ}

Cancel the common factor:

2

= 36 0^{\circ} n + 30 0^{\circ}

2 x = 36 0^{\circ} n + 30 0^{\circ}

2 x = 36 0^{\circ} n + 30 0^{\circ}

2 x = 36 0^{\circ} n + 30 0^{\circ}

Divide both sides by

2

2 x = 36 0^{\circ} n + 30 0^{\circ}

Divide both sides by

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{30 0 ^{\circ}}{2}

Simplify

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{30 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{30 0 ^{\circ}}{2} : 18 0^{\circ} n + 15 0^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{30 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{30 0 ^{\circ}}{2} = 15 0^{\circ}

\frac{30 0 ^{\circ}}{2}

Apply the fraction rule:

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

= \frac{90 0 ^{\circ}}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= 15 0^{\circ}

= 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 15 0^{\circ}

x = 18 0^{\circ} n + 15 0^{\circ}

Popular Examples

cos(x^2)=sin(x^2)

cos (x^{2}) = sin (x^{2})

(cos(-x))/(sin(x))=0

\frac{cos ( - x )}{sin ( x )} = 0

5sin(2x)+3cos(2x)=0,0<= x<= 180

5 sin (2 x) + 3 cos (2 x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

cos(θ)=0.6798,0<= θ<= 360

cos (θ) = 0.6798, 0^{\circ} \leq θ \leq 36 0^{\circ}

(2sin(x)cos(x))/(cos(x))=1

\frac{2 sin ( x ) cos ( x )}{cos ( x )} = 1

Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,1+sin(2x-30)=0 ?
The general solution for solvefor x,1+sin(2x-30)=0 is x=180n+150