What is the general solution for (sin(x-4))(sin(x-1))=0 ?

The general solution for (sin(x-4))(sin(x-1))=0 is x=2pin+4,x=pi+2pin+4,x=2pin+1,x=pi+2pin+1

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Popular >

(sin(x-4))(sin(x-1))=0

Solution

(sin (x - 4)) (sin (x - 1)) = 0

Solution

x = 2 πn + 4, x = π + 2 πn + 4, x = 2 πn + 1, x = π + 2 πn + 1

Degrees

x = 229.18311 \dots^{\circ} + 36 0^{\circ} n, x = 409.18311 \dots^{\circ} + 36 0^{\circ} n, x = 57.29577 \dots^{\circ} + 36 0^{\circ} n, x = 237.29577 \dots^{\circ} + 36 0^{\circ} n

Solution steps

(sin (x - 4)) (sin (x - 1)) = 0

Solving each part separately

sin (x - 4) = 0 or sin (x - 1) = 0

sin (x - 4) = 0 : x = 2 πn + 4, x = π + 2 πn + 4

sin (x - 4) = 0

General solutions for

sin (x - 4) = 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 - 4 = 0 + 2 πn, x - 4 = π + 2 πn

x - 4 = 0 + 2 πn, x - 4 = π + 2 πn

Solve

x - 4 = 0 + 2 πn : x = 2 πn + 4

x - 4 = 0 + 2 πn

0 + 2 πn = 2 πn

x - 4 = 2 πn

Move

4

to the right side

x - 4 = 2 πn

Add

4

to both sides

x - 4 + 4 = 2 πn + 4

Simplify

x = 2 πn + 4

x = 2 πn + 4

Solve

x - 4 = π + 2 πn : x = π + 2 πn + 4

x - 4 = π + 2 πn

Move

4

to the right side

x - 4 = π + 2 πn

Add

4

to both sides

x - 4 + 4 = π + 2 πn + 4

Simplify

x = π + 2 πn + 4

x = π + 2 πn + 4

x = 2 πn + 4, x = π + 2 πn + 4

sin (x - 1) = 0 : x = 2 πn + 1, x = π + 2 πn + 1

sin (x - 1) = 0

General solutions for

sin (x - 1) = 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 - 1 = 0 + 2 πn, x - 1 = π + 2 πn

x - 1 = 0 + 2 πn, x - 1 = π + 2 πn

Solve

x - 1 = 0 + 2 πn : x = 2 πn + 1

x - 1 = 0 + 2 πn

0 + 2 πn = 2 πn

x - 1 = 2 πn

Move

1

to the right side

x - 1 = 2 πn

Add

1

to both sides

x - 1 + 1 = 2 πn + 1

Simplify

x = 2 πn + 1

x = 2 πn + 1

Solve

x - 1 = π + 2 πn : x = π + 2 πn + 1

x - 1 = π + 2 πn

Move

1

to the right side

x - 1 = π + 2 πn

Add

1

to both sides

x - 1 + 1 = π + 2 πn + 1

Simplify

x = π + 2 πn + 1

x = π + 2 πn + 1

x = 2 πn + 1, x = π + 2 πn + 1

Combine all the solutions

x = 2 πn + 4, x = π + 2 πn + 4, x = 2 πn + 1, x = π + 2 πn + 1

Popular Examples

solvefor θ,r=(10)/(3+2cos(θ))solve for

θ, r = \frac{10}{3 + 2 cos ( θ )}

sin(x)=(17.75)/(42)

sin (x) = \frac{17.75}{42}

tan(θ)-sec(θ)=sqrt(3),0<= θ<2pi

tan (θ) - sec (θ) = 3, 0 \leq θ < 2 π

tan(θ)= 5/2 ,0<θ< pi/2 ,sin(θ/2)

tan (θ) = \frac{5}{2}, 0 < θ < \frac{π}{2}, sin (\frac{θ}{2})

3=20.39sin(θ)cos(θ)

3 = 20.39 sin (θ) cos (θ)

Frequently Asked Questions (FAQ)

What is the general solution for (sin(x-4))(sin(x-1))=0 ?
The general solution for (sin(x-4))(sin(x-1))=0 is x=2pin+4,x=pi+2pin+4,x=2pin+1,x=pi+2pin+1