What is the general solution for 6cos(2t)=0 ?

The general solution for 6cos(2t)=0 is t= pi/4+pin,t=(3pi)/4+pin

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6cos(2t)=0

Solution

6 cos (2 t) = 0

Solution

t = \frac{π}{4} + πn, t = \frac{3 π}{4} + πn

Degrees

t = 4 5^{\circ} + 18 0^{\circ} n, t = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

6 cos (2 t) = 0

Divide both sides by

6

6 cos (2 t) = 0

Divide both sides by

6

\frac{6 cos ( 2 t )}{6} = \frac{0}{6}

Simplify

cos (2 t) = 0

cos (2 t) = 0

General solutions for

cos (2 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}

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

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

Solve

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

2 t = \frac{π}{2} + 2 πn

Divide both sides by

2

2 t = \frac{π}{2} + 2 πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 t}{2} : t

\frac{2 t}{2}

Divide the numbers:

\frac{2}{2} = 1

= t

Simplify

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

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

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

= \frac{π}{4} + πn

t = \frac{π}{4} + πn

t = \frac{π}{4} + πn

t = \frac{π}{4} + πn

Solve

2 t = \frac{3 π}{2} + 2 πn : t = \frac{3 π}{4} + πn

2 t = \frac{3 π}{2} + 2 πn

Divide both sides by

2

2 t = \frac{3 π}{2} + 2 πn

Divide both sides by

2

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

Simplify

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

Simplify

\frac{2 t}{2} : t

\frac{2 t}{2}

Divide the numbers:

\frac{2}{2} = 1

= t

Simplify

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} : \frac{3 π}{4} + πn

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

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3 π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

= \frac{3 π}{4} + πn

t = \frac{3 π}{4} + πn

t = \frac{3 π}{4} + πn

t = \frac{3 π}{4} + πn

t = \frac{π}{4} + πn, t = \frac{3 π}{4} + πn

Popular Examples

2cos^2(t)-3cos(t)=-1,0<= t<= 2pi

2 cos^{2} (t) - 3 cos (t) = - 1, 0 \leq t \leq 2 π

4cos(4x)=3

4 cos (4 x) = 3

tan(y)=-2

tan (y) = - 2

sin(θ)=-2/(sqrt(2))

sin (θ) = - \frac{2}{2}

sin^2(x)+sin(x)*cos(x)+cos^2(x)=10

sin^{2} (x) + sin (x) \cdot cos (x) + cos^{2} (x) = 10

Frequently Asked Questions (FAQ)

What is the general solution for 6cos(2t)=0 ?
The general solution for 6cos(2t)=0 is t= pi/4+pin,t=(3pi)/4+pin