English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x^2+3x+5)=0

Solution

sin (x^{2} + 3 x + 5) = 0

Solution

x = \frac{- 3 + 8 πn - 11}{2}, x = \frac{- 3 - 8 πn - 11}{2}, x = \frac{- 3 + 8 πn + 4 π - 11}{2}, x = \frac{- 3 - 8 πn + 4 π - 11}{2}

Degrees

x = - 85.94366 \dots^{\circ} + 107.69755 \dots^{\circ} n, x = - 85.94366 \dots^{\circ} - 107.69755 \dots^{\circ} n, x = - 85.94366 \dots^{\circ} + 148.02703 \dots^{\circ} n, x = - 85.94366 \dots^{\circ} - 148.02703 \dots^{\circ} n

Solution steps

sin (x^{2} + 3 x + 5) = 0

General solutions for

sin (x^{2} + 3 x + 5) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x^{2} + 3 x + 5 = 0 + 2 πn, x^{2} + 3 x + 5 = π + 2 πn

x^{2} + 3 x + 5 = 0 + 2 πn, x^{2} + 3 x + 5 = π + 2 πn

Solve

x^{2} + 3 x + 5 = 0 + 2 πn : x = \frac{- 3 + 8 πn - 11}{2}, x = \frac{- 3 - 8 πn - 11}{2}

x^{2} + 3 x + 5 = 0 + 2 πn

Expand

0 + 2 πn : 2 πn

0 + 2 πn

0 + 2 πn = 2 πn

= 2 πn

x^{2} + 3 x + 5 = 2 πn

Move

2 πn

to the left side

x^{2} + 3 x + 5 = 2 πn

Subtract

2 πn

from both sides

x^{2} + 3 x + 5 - 2 πn = 2 πn - 2 πn

Simplify

x^{2} + 3 x + 5 - 2 πn = 0

x^{2} + 3 x + 5 - 2 πn = 0

Solve with the quadratic formula

x^{2} + 3 x + 5 - 2 πn = 0

Quadratic Equation Formula:

For

a = 1, b = 3, c = 5 - 2 πn

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 1 \cdot ( 5 - 2 πn )}{2 \cdot 1}

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 1 \cdot ( 5 - 2 πn )}{2 \cdot 1}

Simplify

3^{2} - 4 \cdot 1 \cdot (5 - 2 πn) : 8 πn - 11

3^{2} - 4 \cdot 1 \cdot (5 - 2 πn)

Multiply the numbers:

4 \cdot 1 = 4

= 3^{2} - 4 (- 2 πn + 5)

3^{2} = 9

= 9 - 4 (- 2 πn + 5)

Expand

9 - 4 (5 - 2 πn) : 8 πn - 11

9 - 4 (5 - 2 πn)

Expand

- 4 (5 - 2 πn) : - 20 + 8 πn

- 4 (5 - 2 πn)

Apply the distributive law:

a (b - c) = ab - a c

a = - 4, b = 5, c = 2 πn

= - 4 \cdot 5 - (- 4) \cdot 2 πn

Apply minus-plus rules

- (- a) = a

= - 4 \cdot 5 + 4 \cdot 2 πn

Simplify

- 4 \cdot 5 + 4 \cdot 2 πn : - 20 + 8 πn

- 4 \cdot 5 + 4 \cdot 2 πn

Multiply the numbers:

4 \cdot 5 = 20

= - 20 + 4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= - 20 + 8 πn

= - 20 + 8 πn

= 9 - 20 + 8 πn

Subtract the numbers:

9 - 20 = - 11

= 8 πn - 11

= 8 πn - 11

x_{1, 2} = \frac{- 3 \pm 8 πn - 11}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 3 + 8 πn - 11}{2 \cdot 1}, x_{2} = \frac{- 3 - 8 πn - 11}{2 \cdot 1}

x = \frac{- 3 + 8 πn - 11}{2 \cdot 1} : \frac{- 3 + 8 πn - 11}{2}

\frac{- 3 + 8 πn - 11}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{- 3 + 8 πn - 11}{2}

x = \frac{- 3 - 8 πn - 11}{2 \cdot 1} : \frac{- 3 - 8 πn - 11}{2}

\frac{- 3 - 8 πn - 11}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{- 3 - 8 πn - 11}{2}

The solutions to the quadratic equation are:

x = \frac{- 3 + 8 πn - 11}{2}, x = \frac{- 3 - 8 πn - 11}{2}

Solve

x^{2} + 3 x + 5 = π + 2 πn : x = \frac{- 3 + 8 πn + 4 π - 11}{2}, x = \frac{- 3 - 8 πn + 4 π - 11}{2}

x^{2} + 3 x + 5 = π + 2 πn

Move

2 πn

to the left side

x^{2} + 3 x + 5 = π + 2 πn

Subtract

2 πn

from both sides

x^{2} + 3 x + 5 - 2 πn = π + 2 πn - 2 πn

Simplify

x^{2} + 3 x + 5 - 2 πn = π

x^{2} + 3 x + 5 - 2 πn = π

Move

π

to the left side

x^{2} + 3 x + 5 - 2 πn = π

Subtract

π

from both sides

x^{2} + 3 x + 5 - 2 πn - π = π - π

Simplify

x^{2} + 3 x + 5 - 2 πn - π = 0

x^{2} + 3 x + 5 - 2 πn - π = 0

Solve with the quadratic formula

x^{2} + 3 x + 5 - 2 πn - π = 0

Quadratic Equation Formula:

For

a = 1, b = 3, c = 5 - 2 πn - π

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 1 \cdot ( 5 - 2 πn - π )}{2 \cdot 1}

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 1 \cdot ( 5 - 2 πn - π )}{2 \cdot 1}

Simplify

3^{2} - 4 \cdot 1 \cdot (5 - 2 πn - π) : 8 πn + 4 π - 11

3^{2} - 4 \cdot 1 \cdot (5 - 2 πn - π)

Multiply the numbers:

4 \cdot 1 = 4

= 3^{2} - 4 (- 2 πn - π + 5)

3^{2} = 9

= 9 - 4 (- 2 πn - π + 5)

Expand

9 - 4 (5 - 2 πn - π) : 8 πn + 4 π - 11

9 - 4 (5 - 2 πn - π)

Expand

- 4 (5 - 2 πn - π) : - 20 + 8 πn + 4 π

- 4 (5 - 2 πn - π)

Distribute parentheses

= (- 4) \cdot 5 + (- 4) (- 2 πn) + (- 4) (- π)

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - 4 \cdot 5 + 4 \cdot 2 πn + 4 π

Simplify

- 4 \cdot 5 + 4 \cdot 2 πn + 4 π : - 20 + 8 πn + 4 π

- 4 \cdot 5 + 4 \cdot 2 πn + 4 π

Multiply the numbers:

4 \cdot 5 = 20

= - 20 + 4 \cdot 2 πn + 4 π

Multiply the numbers:

4 \cdot 2 = 8

= - 20 + 8 πn + 4 π

= - 20 + 8 πn + 4 π

= 9 - 20 + 8 πn + 4 π

Subtract the numbers:

9 - 20 = - 11

= 8 πn + 4 π - 11

= 8 πn + 4 π - 11

x_{1, 2} = \frac{- 3 \pm 8 πn + 4 π - 11}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 3 + 8 πn + 4 π - 11}{2 \cdot 1}, x_{2} = \frac{- 3 - 8 πn + 4 π - 11}{2 \cdot 1}

x = \frac{- 3 + 8 πn + 4 π - 11}{2 \cdot 1} : \frac{- 3 + 8 πn + 4 π - 11}{2}

\frac{- 3 + 8 πn + 4 π - 11}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{- 3 + 8 πn + 4 π - 11}{2}

x = \frac{- 3 - 8 πn + 4 π - 11}{2 \cdot 1} : \frac{- 3 - 8 πn + 4 π - 11}{2}

\frac{- 3 - 8 πn + 4 π - 11}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{- 3 - 8 πn + 4 π - 11}{2}

The solutions to the quadratic equation are:

x = \frac{- 3 + 8 πn + 4 π - 11}{2}, x = \frac{- 3 - 8 πn + 4 π - 11}{2}

x = \frac{- 3 + 8 πn - 11}{2}, x = \frac{- 3 - 8 πn - 11}{2}, x = \frac{- 3 + 8 πn + 4 π - 11}{2}, x = \frac{- 3 - 8 πn + 4 π - 11}{2}

Graph

Popular Examples

sin(θ)(2sin(θ)+1)=0

sin (θ) (2 sin (θ) + 1) = 0

tan(θ)=0.437

tan (θ) = 0.437

sin(x/3)=-(sqrt(3))/2

sin (\frac{x}{3}) = - \frac{3}{2}

2cos(x)+3=2

2 cos (x) + 3 = 2

6sin^2(x)=3

6 sin^{2} (x) = 3