What is the general solution for cos^2(x)=-0.5 ?

The general solution for cos^2(x)=-0.5 is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^2(x)=-0.5

cos^{2} (x) = - 0.5

No Solution for x \in R

Solution steps

cos^{2} (x) = - 0.5

Solve by substitution

cos^{2} (x) = - 0.5

Let:

cos (x) = u

u^{2} = - 0.5

u^{2} = - 0.5 : u = 0.5 i, u = - 0.5 i

u^{2} = - 0.5

For

x^{2} = f (a)

the solutions are

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

u = - 0.5, u = - - 0.5

Simplify

- 0.5 : 0.5 i

- 0.5

Apply radical rule:

- a = - 1 a

- 0.5 = - 1 0.5

= - 1 0.5

Apply imaginary number rule:

- 1 = i

= 0.5 i

Simplify

- - 0.5 : - 0.5 i

- - 0.5

Simplify

- 0.5 : 0.5 i

- 0.5

Apply radical rule:

- a = - 1 a

- 0.5 = - 1 0.5

= - 1 0.5

Apply imaginary number rule:

- 1 = i

= 0.5 i

= - 0.5 i

u = 0.5 i, u = - 0.5 i

Substitute back

u = cos (x)

cos (x) = 0.5 i, cos (x) = - 0.5 i

cos (x) = 0.5 i, cos (x) = - 0.5 i

cos (x) = 0.5 i :

No Solution

cos (x) = 0.5 i

No Solution

cos (x) = - 0.5 i :

No Solution

cos (x) = - 0.5 i

No Solution

Combine all the solutions

No Solution for x \in R

cos (x) = \frac{1.5}{4.272}

\frac{π}{12} = arcsin (\frac{x}{2})

6 sin^{2} (x) = 0

\frac{1 - tanh ( x )}{1 + tanh ( x )} = 2

40 = tan (ln (18 + 1) + C)

What is the general solution for cos^2(x)=-0.5 ?
The general solution for cos^2(x)=-0.5 is No Solution for x\in\mathbb{R}