What is the general solution for 2sin^2(x)-2=0 ?

The general solution for 2sin^2(x)-2=0 is x= pi/2+2pin,x=(3pi)/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin^2(x)-2=0

Solution

2 sin^{2} (x) - 2 = 0

Solution

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

Degrees

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

Solution steps

2 sin^{2} (x) - 2 = 0

Solve by substitution

2 sin^{2} (x) - 2 = 0

Let:

sin (x) = u

2 u^{2} - 2 = 0

2 u^{2} - 2 = 0 : u = 1, u = - 1

2 u^{2} - 2 = 0

Move

2

to the right side

2 u^{2} - 2 = 0

Add

2

to both sides

2 u^{2} - 2 + 2 = 0 + 2

Simplify

2 u^{2} = 2

2 u^{2} = 2

Divide both sides by

2

2 u^{2} = 2

Divide both sides by

2

\frac{2 u ^{2}}{2} = \frac{2}{2}

Simplify

u^{2} = 1

u^{2} = 1

For

x^{2} = f (a)

the solutions are

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

u = 1, u = - 1

1 = 1

1

Apply rule

1 = 1

= 1

- 1 = - 1

- 1

Apply rule

1 = 1

= - 1

u = 1, u = - 1

Substitute back

u = sin (x)

sin (x) = 1, sin (x) = - 1

sin (x) = 1, sin (x) = - 1

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = 1

General solutions for

sin (x) = 1

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 = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = - 1

General solutions for

sin (x) = - 1

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 = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

Popular Examples

2tan^2(x)=13

2 tan^{2} (x) = 13

2tan^2(x)=15

2 tan^{2} (x) = 15

1-cos(θ)=1+cos(θ)

1 - cos (θ) = 1 + cos (θ)

cos(2x)+cos(x)=1

cos (2 x) + cos (x) = 1

tan(x)sec(x)=-2tan(x)

tan (x) sec (x) = - 2 tan (x)

Frequently Asked Questions (FAQ)

What is the general solution for 2sin^2(x)-2=0 ?
The general solution for 2sin^2(x)-2=0 is x= pi/2+2pin,x=(3pi)/2+2pin