English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x^2)=-(sqrt(2))/2

Solution

cos (x^{2}) = - \frac{2}{2}

Solution

x = \frac{3 π + 8 πn}{2}, x = - \frac{3 π + 8 πn}{2}, x = \frac{5 π + 8 πn}{2}, x = - \frac{5 π + 8 πn}{2}

Degrees

x = 0^{\circ} + 168.40846 \dots^{\circ} n, x = 0^{\circ} - 168.40846 \dots^{\circ} n, x = 0^{\circ} + 183.07930 \dots^{\circ} n, x = 0^{\circ} - 183.07930 \dots^{\circ} n

Solution steps

cos (x^{2}) = - \frac{2}{2}

General solutions for

cos (x^{2}) = - \frac{2}{2}

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

x^{2} = \frac{3 π}{4} + 2 πn, x^{2} = \frac{5 π}{4} + 2 πn

x^{2} = \frac{3 π}{4} + 2 πn, x^{2} = \frac{5 π}{4} + 2 πn

Solve

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

x^{2} = \frac{3 π}{4} + 2 πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

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

Simplify

\frac{3 π}{4} + 2 πn : \frac{3 π + 8 πn}{2}

\frac{3 π}{4} + 2 πn

Join

\frac{3 π}{4} + 2 πn : \frac{3 π + 8 πn}{4}

\frac{3 π}{4} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 4}{4}

= \frac{3 π}{4} + \frac{2 πn \cdot 4}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{3 π + 2 πn \cdot 4}{4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{3 π + 8 πn}{4}

= \frac{3 π + 8 πn}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{3 π + 8 πn}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{3 π + 8 πn}{2}

Simplify

- \frac{3 π}{4} + 2 πn : - \frac{3 π + 8 πn}{2}

- \frac{3 π}{4} + 2 πn

Join

\frac{3 π}{4} + 2 πn : \frac{3 π + 8 πn}{4}

\frac{3 π}{4} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 4}{4}

= \frac{3 π}{4} + \frac{2 πn \cdot 4}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{3 π + 2 πn \cdot 4}{4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{3 π + 8 πn}{4}

= - \frac{3 π + 8 πn}{4}

Simplify

\frac{3 π + 8 πn}{4} : \frac{3 π + 8 πn}{2}

\frac{3 π + 8 πn}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{3 π + 8 πn}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{3 π + 8 πn}{2}

= - \frac{3 π + 8 πn}{2}

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

Solve

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

x^{2} = \frac{5 π}{4} + 2 πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{5 π}{4} + 2 πn, x = - \frac{5 π}{4} + 2 πn

Simplify

\frac{5 π}{4} + 2 πn : \frac{5 π + 8 πn}{2}

\frac{5 π}{4} + 2 πn

Join

\frac{5 π}{4} + 2 πn : \frac{5 π + 8 πn}{4}

\frac{5 π}{4} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 4}{4}

= \frac{5 π}{4} + \frac{2 πn \cdot 4}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{5 π + 2 πn \cdot 4}{4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{5 π + 8 πn}{4}

= \frac{5 π + 8 πn}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{5 π + 8 πn}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{5 π + 8 πn}{2}

Simplify

- \frac{5 π}{4} + 2 πn : - \frac{5 π + 8 πn}{2}

- \frac{5 π}{4} + 2 πn

Join

\frac{5 π}{4} + 2 πn : \frac{5 π + 8 πn}{4}

\frac{5 π}{4} + 2 πn

Convert element to fraction:

2 πn = \frac{2 πn 4}{4}

= \frac{5 π}{4} + \frac{2 πn \cdot 4}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{5 π + 2 πn \cdot 4}{4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{5 π + 8 πn}{4}

= - \frac{5 π + 8 πn}{4}

Simplify

\frac{5 π + 8 πn}{4} : \frac{5 π + 8 πn}{2}

\frac{5 π + 8 πn}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{5 π + 8 πn}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{5 π + 8 πn}{2}

= - \frac{5 π + 8 πn}{2}

x = \frac{5 π + 8 πn}{2}, x = - \frac{5 π + 8 πn}{2}

x = \frac{3 π + 8 πn}{2}, x = - \frac{3 π + 8 πn}{2}, x = \frac{5 π + 8 πn}{2}, x = - \frac{5 π + 8 πn}{2}

Popular Examples

sin(α)=(sqrt(3))/2

sin (α) = \frac{3}{2}

solvefor x,sin(x/x)=1 solve for

x, sin (\frac{x}{x}) = 1

4sin(θ)+4=0

4 sin (θ) + 4 = 0

sin^2(a)+2cos(a)= 49/25

sin^{2} (a) + 2 cos (a) = \frac{49}{25}

cot(x)+csc(x)=1

cot (x) + csc (x) = 1