What is the general solution for 0=6cos(3t) ?

The general solution for 0=6cos(3t) is t= pi/6+(2pin)/3 ,t= pi/2+(2pin)/3

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0=6cos(3t)

Solution

0 = 6 cos (3 t)

Solution

t = \frac{π}{6} + \frac{2 πn}{3}, t = \frac{π}{2} + \frac{2 πn}{3}

Degrees

t = 3 0^{\circ} + 12 0^{\circ} n, t = 9 0^{\circ} + 12 0^{\circ} n

Solution steps

0 = 6 cos (3 t)

Switch sides

6 cos (3 t) = 0

Divide both sides by

6

6 cos (3 t) = 0

Divide both sides by

6

\frac{6 cos ( 3 t )}{6} = \frac{0}{6}

Simplify

cos (3 t) = 0

cos (3 t) = 0

General solutions for

cos (3 t) = 0

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

Solve

3 t = \frac{π}{2} + 2 πn : t = \frac{π}{6} + \frac{2 πn}{3}

3 t = \frac{π}{2} + 2 πn

Divide both sides by

3

3 t = \frac{π}{2} + 2 πn

Divide both sides by

3

\frac{3 t}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 t}{3} = \frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 t}{3} : t

\frac{3 t}{3}

Divide the numbers:

\frac{3}{3} = 1

= t

Simplify

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3} : \frac{π}{6} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} + \frac{2 πn}{3}

\frac{\frac{π}{2}}{3} = \frac{π}{6}

\frac{\frac{π}{2}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{3}

t = \frac{π}{6} + \frac{2 πn}{3}

t = \frac{π}{6} + \frac{2 πn}{3}

t = \frac{π}{6} + \frac{2 πn}{3}

Solve

3 t = \frac{3 π}{2} + 2 πn : t = \frac{π}{2} + \frac{2 πn}{3}

3 t = \frac{3 π}{2} + 2 πn

Divide both sides by

3

3 t = \frac{3 π}{2} + 2 πn

Divide both sides by

3

\frac{3 t}{3} = \frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 t}{3} = \frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

Simplify

\frac{3 t}{3} : t

\frac{3 t}{3}

Divide the numbers:

\frac{3}{3} = 1

= t

Simplify

\frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3} : \frac{π}{2} + \frac{2 πn}{3}

\frac{\frac{3 π}{2}}{3} + \frac{2 πn}{3}

\frac{\frac{3 π}{2}}{3} = \frac{π}{2}

\frac{\frac{3 π}{2}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{3 π}{6}

Cancel the common factor:

3

= \frac{π}{2}

= \frac{π}{2} + \frac{2 πn}{3}

t = \frac{π}{2} + \frac{2 πn}{3}

t = \frac{π}{2} + \frac{2 πn}{3}

t = \frac{π}{2} + \frac{2 πn}{3}

t = \frac{π}{6} + \frac{2 πn}{3}, t = \frac{π}{2} + \frac{2 πn}{3}

Popular Examples

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

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

cos(z)= 5/4

cos (z) = \frac{5}{4}

cos(B)= 3/8

cos (B) = \frac{3}{8}

sin(2x)=-3/2

sin (2 x) = - \frac{3}{2}

2sin^2(1/2 x)+C=-2cos(x/2)sin(x/2)+C

2 sin^{2} (\frac{1}{2} x) + C = - 2 cos (\frac{x}{2}) sin (\frac{x}{2}) + C

Frequently Asked Questions (FAQ)

What is the general solution for 0=6cos(3t) ?
The general solution for 0=6cos(3t) is t= pi/6+(2pin)/3 ,t= pi/2+(2pin)/3