What is the general solution for cos(5/2 x)=0 ?

The general solution for cos(5/2 x)=0 is x= pi/5+(4pin)/5 ,x=(3pi)/5+(4pin)/5

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cos(5/2 x)=0

Solution

cos (\frac{5}{2} x) = 0

Solution

x = \frac{π}{5} + \frac{4 πn}{5}, x = \frac{3 π}{5} + \frac{4 πn}{5}

Degrees

x = 3 6^{\circ} + 14 4^{\circ} n, x = 10 8^{\circ} + 14 4^{\circ} n

Solution steps

cos (\frac{5}{2} x) = 0

General solutions for

cos (\frac{5}{2} x) = 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}

\frac{5}{2} x = \frac{π}{2} + 2 πn, \frac{5}{2} x = \frac{3 π}{2} + 2 πn

\frac{5}{2} x = \frac{π}{2} + 2 πn, \frac{5}{2} x = \frac{3 π}{2} + 2 πn

Solve

\frac{5}{2} x = \frac{π}{2} + 2 πn : x = \frac{π}{5} + \frac{4 πn}{5}

\frac{5}{2} x = \frac{π}{2} + 2 πn

Multiply both sides by

2

\frac{5}{2} x = \frac{π}{2} + 2 πn

Multiply both sides by

2

2 \cdot \frac{5}{2} x = 2 \cdot \frac{π}{2} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{5}{2} x = 2 \cdot \frac{π}{2} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{5}{2} x : 5 x

2 \cdot \frac{5}{2} x

Multiply fractions:

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

= \frac{5 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 5

Simplify

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

2 \cdot \frac{π}{2} + 2 \cdot 2 πn

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 2}{2}

Cancel the common factor:

2

= π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= π + 4 πn

5 x = π + 4 πn

5 x = π + 4 πn

5 x = π + 4 πn

Divide both sides by

5

5 x = π + 4 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{π}{5} + \frac{4 πn}{5}

Simplify

x = \frac{π}{5} + \frac{4 πn}{5}

x = \frac{π}{5} + \frac{4 πn}{5}

Solve

\frac{5}{2} x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{5} + \frac{4 πn}{5}

\frac{5}{2} x = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

\frac{5}{2} x = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

2 \cdot \frac{5}{2} x = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{5}{2} x = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{5}{2} x : 5 x

2 \cdot \frac{5}{2} x

Multiply fractions:

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

= \frac{5 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 5

Simplify

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

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

2 \cdot \frac{3 π}{2} = 3 π

2 \cdot \frac{3 π}{2}

Multiply fractions:

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

= \frac{3 π 2}{2}

Cancel the common factor:

2

= 3 π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= 3 π + 4 πn

5 x = 3 π + 4 πn

5 x = 3 π + 4 πn

5 x = 3 π + 4 πn

Divide both sides by

5

5 x = 3 π + 4 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{3 π}{5} + \frac{4 πn}{5}

Simplify

x = \frac{3 π}{5} + \frac{4 πn}{5}

x = \frac{3 π}{5} + \frac{4 πn}{5}

x = \frac{π}{5} + \frac{4 πn}{5}, x = \frac{3 π}{5} + \frac{4 πn}{5}

Popular Examples

sin(5x)=sin(7x)

sin (5 x) = sin (7 x)

cos(x)=0,60

cos (x) = 0, 60

cos(2x)-sin^2(x)=cos^2(x)

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

cos(x)=0,56

cos (x) = 0, 56

cos(x/2)= 5/6

cos (\frac{x}{2}) = \frac{5}{6}

Frequently Asked Questions (FAQ)

What is the general solution for cos(5/2 x)=0 ?
The general solution for cos(5/2 x)=0 is x= pi/5+(4pin)/5 ,x=(3pi)/5+(4pin)/5