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Popular >

sin(x^2+1)=0

Solution

sin (x^{2} + 1) = 0

Solution

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

+1

Degrees

x = 0^{\circ} + 131.69538 \dots^{\circ} n, x = 0^{\circ} - 131.69538 \dots^{\circ} n, x = 0^{\circ} + 166.30368 \dots^{\circ} n, x = 0^{\circ} - 166.30368 \dots^{\circ} n

Solution steps

sin (x^{2} + 1) = 0

General solutions for

sin (x^{2} + 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^{2} + 1 = 0 + 2 πn, x^{2} + 1 = π + 2 πn

x^{2} + 1 = 0 + 2 πn, x^{2} + 1 = π + 2 πn

Solve

x^{2} + 1 = 0 + 2 πn : x = 2 πn - 1, x = - 2 πn - 1

x^{2} + 1 = 0 + 2 πn

Move

1

to the right side

x^{2} + 1 = 0 + 2 πn

Subtract

1

from both sides

x^{2} + 1 - 1 = 0 + 2 πn - 1

Simplify

x^{2} = 2 πn - 1

x^{2} = 2 πn - 1

For

x^{2} = f (a)

the solutions are

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

x = 2 πn - 1, x = - 2 πn - 1

Solve

x^{2} + 1 = π + 2 πn : x = π + 2 πn - 1, x = - π + 2 πn - 1

x^{2} + 1 = π + 2 πn

Move

1

to the right side

x^{2} + 1 = π + 2 πn

Subtract

1

from both sides

x^{2} + 1 - 1 = π + 2 πn - 1

Simplify

x^{2} = π + 2 πn - 1

x^{2} = π + 2 πn - 1

For

x^{2} = f (a)

the solutions are

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

x = π + 2 πn - 1, x = - π + 2 πn - 1

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

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