What is the general solution for 1/4 sin(4t)=0 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/4 sin(4t)=0

\frac{1}{4} sin (4 t) = 0

t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

Degrees

t = 0^{\circ} + 9 0^{\circ} n, t = 4 5^{\circ} + 9 0^{\circ} n

Solution steps

\frac{1}{4} sin (4 t) = 0

Multiply both sides by

4

\frac{1}{4} sin (4 t) = 0

Multiply both sides by

4

4 \cdot \frac{1}{4} sin (4 t) = 0 \cdot 4

Simplify

sin (4 t) = 0

sin (4 t) = 0

General solutions for

sin (4 t) = 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}

4 t = 0 + 2 πn, 4 t = π + 2 πn

4 t = 0 + 2 πn, 4 t = π + 2 πn

Solve

4 t = 0 + 2 πn : t = \frac{πn}{2}

4 t = 0 + 2 πn

0 + 2 πn = 2 πn

4 t = 2 πn

Divide both sides by

4

4 t = 2 πn

Divide both sides by

4

\frac{4 t}{4} = \frac{2 πn}{4}

Simplify

t = \frac{πn}{2}

t = \frac{πn}{2}

Solve

4 t = π + 2 πn : t = \frac{π}{4} + \frac{πn}{2}

4 t = π + 2 πn

Divide both sides by

4

4 t = π + 2 πn

Divide both sides by

4

\frac{4 t}{4} = \frac{π}{4} + \frac{2 πn}{4}

Simplify

t = \frac{π}{4} + \frac{πn}{2}

t = \frac{π}{4} + \frac{πn}{2}

t = \frac{πn}{2}, t = \frac{π}{4} + \frac{πn}{2}

csc (x) + 2 = 0, (0, 2 π)

2 cos (4 x) = 2 cos^{2} (2 x) - sin (2 x) - 1

x, sin (x - 4 0^{\circ}) = cos (y - 2 0^{\circ})

0 = - sin (2 x)

1 - sin^{2} (θ) = 0

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