What is the general solution for 3*cos(4θ)=0 ?

The general solution for 3*cos(4θ)=0 is θ= pi/8+(pin)/2 ,θ=(3pi)/8+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3*cos(4θ)=0

Solution

3 \cdot cos (4 θ) = 0

Solution

θ = \frac{π}{8} + \frac{πn}{2}, θ = \frac{3 π}{8} + \frac{πn}{2}

Degrees

θ = 22. 5^{\circ} + 9 0^{\circ} n, θ = 67. 5^{\circ} + 9 0^{\circ} n

Solution steps

3 cos (4 θ) = 0

Divide both sides by

3

3 cos (4 θ) = 0

Divide both sides by

3

\frac{3 cos ( 4 θ )}{3} = \frac{0}{3}

Simplify

cos (4 θ) = 0

cos (4 θ) = 0

General solutions for

cos (4 θ) = 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}

4 θ = \frac{π}{2} + 2 πn, 4 θ = \frac{3 π}{2} + 2 πn

4 θ = \frac{π}{2} + 2 πn, 4 θ = \frac{3 π}{2} + 2 πn

Solve

4 θ = \frac{π}{2} + 2 πn : θ = \frac{π}{8} + \frac{πn}{2}

4 θ = \frac{π}{2} + 2 πn

Divide both sides by

4

4 θ = \frac{π}{2} + 2 πn

Divide both sides by

4

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

Simplify

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

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

\frac{\frac{π}{2}}{4} + \frac{2 πn}{4} : \frac{π}{8} + \frac{πn}{2}

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

\frac{\frac{π}{2}}{4} = \frac{π}{8}

\frac{\frac{π}{2}}{4}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{π}{8}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{8} + \frac{πn}{2}

θ = \frac{π}{8} + \frac{πn}{2}

θ = \frac{π}{8} + \frac{πn}{2}

θ = \frac{π}{8} + \frac{πn}{2}

Solve

4 θ = \frac{3 π}{2} + 2 πn : θ = \frac{3 π}{8} + \frac{πn}{2}

4 θ = \frac{3 π}{2} + 2 πn

Divide both sides by

4

4 θ = \frac{3 π}{2} + 2 πn

Divide both sides by

4

\frac{4 θ}{4} = \frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4}

Simplify

\frac{4 θ}{4} = \frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4}

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

\frac{\frac{3 π}{2}}{4} + \frac{2 πn}{4} : \frac{3 π}{8} + \frac{πn}{2}

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

\frac{\frac{3 π}{2}}{4} = \frac{3 π}{8}

\frac{\frac{3 π}{2}}{4}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{3 π}{8}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{π}{8} + \frac{πn}{2}, θ = \frac{3 π}{8} + \frac{πn}{2}

Popular Examples

5tan(x)-5=0

5 tan (x) - 5 = 0

-4sin(x)+3cos(x)=0

- 4 sin (x) + 3 cos (x) = 0

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

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

2sqrt(3)cos(2x)=-3

23 cos (2 x) = - 3

3cos(x)+sin(x)=1

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

Frequently Asked Questions (FAQ)

What is the general solution for 3*cos(4θ)=0 ?
The general solution for 3*cos(4θ)=0 is θ= pi/8+(pin)/2 ,θ=(3pi)/8+(pin)/2