What is the general solution for 12sin(x)-sqrt(2)=sqrt(2)+8sin(x) ?

The general solution for 12sin(x)-sqrt(2)=sqrt(2)+8sin(x) is x= pi/4+2pin,x=(3pi)/4+2pin

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Popular >

12sin(x)-sqrt(2)=sqrt(2)+8sin(x)

Solution

12 sin (x) - 2 = 2 + 8 sin (x)

Solution

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

Degrees

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

12 sin (x) - 2 = 2 + 8 sin (x)

Solve by substitution

12 sin (x) - 2 = 2 + 8 sin (x)

Let:

sin (x) = u

12 u - 2 = 2 + 8 u

12 u - 2 = 2 + 8 u : u = \frac{2}{2}

12 u - 2 = 2 + 8 u

Move

2

to the right side

12 u - 2 = 2 + 8 u

Add

2

to both sides

12 u - 2 + 2 = 2 + 8 u + 2

Simplify

12 u - 2 + 2 = 2 + 8 u + 2

Simplify

12 u - 2 + 2 : 12 u

12 u - 2 + 2

Add similar elements:

- 2 + 2 = 0

= 12 u

Simplify

2 + 8 u + 2 : 8 u + 22

2 + 8 u + 2

Group like terms

= 8 u + 2 + 2

Add similar elements:

2 + 2 = 22

= 8 u + 22

12 u = 8 u + 22

12 u = 8 u + 22

12 u = 8 u + 22

Move

8 u

to the left side

12 u = 8 u + 22

Subtract

8 u

from both sides

12 u - 8 u = 8 u + 22 - 8 u

Simplify

4 u = 22

4 u = 22

Divide both sides by

4

4 u = 22

Divide both sides by

4

\frac{4 u}{4} = \frac{2 2}{4}

Simplify

u = \frac{2}{2}

u = \frac{2}{2}

Substitute back

u = sin (x)

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

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

sin (x) = \frac{2}{2} : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

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

General solutions for

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

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}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

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

Combine all the solutions

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

Popular Examples

cos(2x+30)= 1/2 ,0<= x<= 360

cos (2 x + 30) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

tan(θ)= 43/90

tan (θ) = \frac{43}{90}

2sin(2x+pi/3)=1

2 sin (2 x + \frac{π}{3}) = 1

sec(x)=2,cos(x)

sec (x) = 2, cos (x)

-cosh(sech(x))(sech(x)tanh(x))=0

- cosh (sech (x)) (sech (x) tanh (x)) = 0

Frequently Asked Questions (FAQ)

What is the general solution for 12sin(x)-sqrt(2)=sqrt(2)+8sin(x) ?
The general solution for 12sin(x)-sqrt(2)=sqrt(2)+8sin(x) is x= pi/4+2pin,x=(3pi)/4+2pin