What is the general solution for cos(10x)=0 ?

The general solution for cos(10x)=0 is x= pi/(20)+(pin)/5 ,x=(3pi}{20}+\frac{pin)/5

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cos(10x)=0

Solution

cos (10 x) = 0

Solution

x = \frac{π}{20} + \frac{πn}{5}, x = \frac{3 π}{20} + \frac{πn}{5}

Degrees

x = 9^{\circ} + 3 6^{\circ} n, x = 2 7^{\circ} + 3 6^{\circ} n

Solution steps

cos (10 x) = 0

General solutions for

cos (10 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}

10 x = \frac{π}{2} + 2 πn, 10 x = \frac{3 π}{2} + 2 πn

10 x = \frac{π}{2} + 2 πn, 10 x = \frac{3 π}{2} + 2 πn

Solve

10 x = \frac{π}{2} + 2 πn : x = \frac{π}{20} + \frac{πn}{5}

10 x = \frac{π}{2} + 2 πn

Divide both sides by

10

10 x = \frac{π}{2} + 2 πn

Divide both sides by

10

\frac{10 x}{10} = \frac{\frac{π}{2}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 x}{10} = \frac{\frac{π}{2}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 x}{10} : x

\frac{10 x}{10}

Divide the numbers:

\frac{10}{10} = 1

= x

Simplify

\frac{\frac{π}{2}}{10} + \frac{2 πn}{10} : \frac{π}{20} + \frac{πn}{5}

\frac{\frac{π}{2}}{10} + \frac{2 πn}{10}

\frac{\frac{π}{2}}{10} = \frac{π}{20}

\frac{\frac{π}{2}}{10}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 10}

Multiply the numbers:

2 \cdot 10 = 20

= \frac{π}{20}

\frac{2 πn}{10} = \frac{πn}{5}

\frac{2 πn}{10}

Cancel the common factor:

2

= \frac{πn}{5}

= \frac{π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}

Solve

10 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{20} + \frac{πn}{5}

10 x = \frac{3 π}{2} + 2 πn

Divide both sides by

10

10 x = \frac{3 π}{2} + 2 πn

Divide both sides by

10

\frac{10 x}{10} = \frac{\frac{3 π}{2}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 x}{10} = \frac{\frac{3 π}{2}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 x}{10} : x

\frac{10 x}{10}

Divide the numbers:

\frac{10}{10} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{10} + \frac{2 πn}{10} : \frac{3 π}{20} + \frac{πn}{5}

\frac{\frac{3 π}{2}}{10} + \frac{2 πn}{10}

\frac{\frac{3 π}{2}}{10} = \frac{3 π}{20}

\frac{\frac{3 π}{2}}{10}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 10}

Multiply the numbers:

2 \cdot 10 = 20

= \frac{3 π}{20}

\frac{2 πn}{10} = \frac{πn}{5}

\frac{2 πn}{10}

Cancel the common factor:

2

= \frac{πn}{5}

= \frac{3 π}{20} + \frac{πn}{5}

x = \frac{3 π}{20} + \frac{πn}{5}

x = \frac{3 π}{20} + \frac{πn}{5}

x = \frac{3 π}{20} + \frac{πn}{5}

x = \frac{π}{20} + \frac{πn}{5}, x = \frac{3 π}{20} + \frac{πn}{5}

Popular Examples

7-5cos(x)=10

7 - 5 cos (x) = 10

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sin^{2} (θ) - 2 = sin (θ)

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5 + 4 cos (x) = 0

csc^2(x)-csc(x)-2=0,0<= x<= 2pi

csc^{2} (x) - csc (x) - 2 = 0, 0 \leq x \leq 2 π

sinh(x-1)=0

sinh (x - 1) = 0

Frequently Asked Questions (FAQ)

What is the general solution for cos(10x)=0 ?
The general solution for cos(10x)=0 is x= pi/(20)+(pin)/5 ,x=(3pi}{20}+\frac{pin)/5