What is the general solution for cos(16x)=0 ?

The general solution for cos(16x)=0 is x= pi/(32)+(pin)/8 ,x=(3pi}{32}+\frac{pin)/8

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cos(16x)=0

Solution

cos (16 x) = 0

Solution

x = \frac{π}{32} + \frac{πn}{8}, x = \frac{3 π}{32} + \frac{πn}{8}

Degrees

x = 5.62 5^{\circ} + 22. 5^{\circ} n, x = 16.87 5^{\circ} + 22. 5^{\circ} n

Solution steps

cos (16 x) = 0

General solutions for

cos (16 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}

16 x = \frac{π}{2} + 2 πn, 16 x = \frac{3 π}{2} + 2 πn

16 x = \frac{π}{2} + 2 πn, 16 x = \frac{3 π}{2} + 2 πn

Solve

16 x = \frac{π}{2} + 2 πn : x = \frac{π}{32} + \frac{πn}{8}

16 x = \frac{π}{2} + 2 πn

Divide both sides by

16

16 x = \frac{π}{2} + 2 πn

Divide both sides by

16

\frac{16 x}{16} = \frac{\frac{π}{2}}{16} + \frac{2 πn}{16}

Simplify

\frac{16 x}{16} = \frac{\frac{π}{2}}{16} + \frac{2 πn}{16}

Simplify

\frac{16 x}{16} : x

\frac{16 x}{16}

Divide the numbers:

\frac{16}{16} = 1

= x

Simplify

\frac{\frac{π}{2}}{16} + \frac{2 πn}{16} : \frac{π}{32} + \frac{πn}{8}

\frac{\frac{π}{2}}{16} + \frac{2 πn}{16}

\frac{\frac{π}{2}}{16} = \frac{π}{32}

\frac{\frac{π}{2}}{16}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 16}

Multiply the numbers:

2 \cdot 16 = 32

= \frac{π}{32}

\frac{2 πn}{16} = \frac{πn}{8}

\frac{2 πn}{16}

Cancel the common factor:

2

= \frac{πn}{8}

= \frac{π}{32} + \frac{πn}{8}

x = \frac{π}{32} + \frac{πn}{8}

x = \frac{π}{32} + \frac{πn}{8}

x = \frac{π}{32} + \frac{πn}{8}

Solve

16 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{32} + \frac{πn}{8}

16 x = \frac{3 π}{2} + 2 πn

Divide both sides by

16

16 x = \frac{3 π}{2} + 2 πn

Divide both sides by

16

\frac{16 x}{16} = \frac{\frac{3 π}{2}}{16} + \frac{2 πn}{16}

Simplify

\frac{16 x}{16} = \frac{\frac{3 π}{2}}{16} + \frac{2 πn}{16}

Simplify

\frac{16 x}{16} : x

\frac{16 x}{16}

Divide the numbers:

\frac{16}{16} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{16} + \frac{2 πn}{16} : \frac{3 π}{32} + \frac{πn}{8}

\frac{\frac{3 π}{2}}{16} + \frac{2 πn}{16}

\frac{\frac{3 π}{2}}{16} = \frac{3 π}{32}

\frac{\frac{3 π}{2}}{16}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 16}

Multiply the numbers:

2 \cdot 16 = 32

= \frac{3 π}{32}

\frac{2 πn}{16} = \frac{πn}{8}

\frac{2 πn}{16}

Cancel the common factor:

2

= \frac{πn}{8}

= \frac{3 π}{32} + \frac{πn}{8}

x = \frac{3 π}{32} + \frac{πn}{8}

x = \frac{3 π}{32} + \frac{πn}{8}

x = \frac{3 π}{32} + \frac{πn}{8}

x = \frac{π}{32} + \frac{πn}{8}, x = \frac{3 π}{32} + \frac{πn}{8}

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Frequently Asked Questions (FAQ)

What is the general solution for cos(16x)=0 ?
The general solution for cos(16x)=0 is x= pi/(32)+(pin)/8 ,x=(3pi}{32}+\frac{pin)/8