What is the general solution for cos((2x-pi)/(17))=0 ?

The general solution for cos((2x-pi)/(17))=0 is x=17pin+pi/2+(17pi)/4 ,x=17pin+pi/2+(51pi)/4

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cos((2x-pi)/(17))=0

Solution

cos (\frac{2 x - π}{17}) = 0

Solution

x = 17 πn + \frac{π}{2} + \frac{17 π}{4}, x = 17 πn + \frac{π}{2} + \frac{51 π}{4}

Degrees

x = 85 5^{\circ} + 306 0^{\circ} n, x = 238 5^{\circ} + 306 0^{\circ} n

Solution steps

cos (\frac{2 x - π}{17}) = 0

General solutions for

cos (\frac{2 x - π}{17}) = 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{2 x - π}{17} = \frac{π}{2} + 2 πn, \frac{2 x - π}{17} = \frac{3 π}{2} + 2 πn

\frac{2 x - π}{17} = \frac{π}{2} + 2 πn, \frac{2 x - π}{17} = \frac{3 π}{2} + 2 πn

Solve

\frac{2 x - π}{17} = \frac{π}{2} + 2 πn : x = 17 πn + \frac{π}{2} + \frac{17 π}{4}

\frac{2 x - π}{17} = \frac{π}{2} + 2 πn

Multiply both sides by

17

\frac{2 x - π}{17} = \frac{π}{2} + 2 πn

Multiply both sides by

17

\frac{17 ( 2 x - π )}{17} = 17 \cdot \frac{π}{2} + 17 \cdot 2 πn

Simplify

\frac{17 ( 2 x - π )}{17} = 17 \cdot \frac{π}{2} + 17 \cdot 2 πn

Simplify

\frac{17 ( 2 x - π )}{17} : 2 x - π

\frac{17 ( 2 x - π )}{17}

Divide the numbers:

\frac{17}{17} = 1

= 2 x - π

Simplify

17 \cdot \frac{π}{2} + 17 \cdot 2 πn : \frac{17 π}{2} + 34 πn

17 \cdot \frac{π}{2} + 17 \cdot 2 πn

Multiply

17 \cdot \frac{π}{2} : \frac{17 π}{2}

17 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 17}{2}

= \frac{17 π}{2} + 17 \cdot 2 πn

Multiply the numbers:

17 \cdot 2 = 34

= \frac{17 π}{2} + 34 πn

2 x - π = \frac{17 π}{2} + 34 πn

2 x - π = \frac{17 π}{2} + 34 πn

2 x - π = \frac{17 π}{2} + 34 πn

Move

π

to the right side

2 x - π = \frac{17 π}{2} + 34 πn

Add

π

to both sides

2 x - π + π = \frac{17 π}{2} + 34 πn + π

Simplify

2 x = \frac{17 π}{2} + 34 πn + π

2 x = \frac{17 π}{2} + 34 πn + π

Divide both sides by

2

2 x = \frac{17 π}{2} + 34 πn + π

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{17 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{17 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{17 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2} : 17 πn + \frac{π}{2} + \frac{17 π}{4}

\frac{\frac{17 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2}

Group like terms

= \frac{π}{2} + \frac{34 πn}{2} + \frac{\frac{17 π}{2}}{2}

\frac{34 πn}{2} = 17 πn

\frac{34 πn}{2}

Divide the numbers:

\frac{34}{2} = 17

= 17 πn

\frac{\frac{17 π}{2}}{2} = \frac{17 π}{4}

\frac{\frac{17 π}{2}}{2}

Apply the fraction rule:

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

= \frac{17 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{17 π}{4}

= \frac{π}{2} + 17 πn + \frac{17 π}{4}

Group like terms

= 17 πn + \frac{π}{2} + \frac{17 π}{4}

x = 17 πn + \frac{π}{2} + \frac{17 π}{4}

x = 17 πn + \frac{π}{2} + \frac{17 π}{4}

x = 17 πn + \frac{π}{2} + \frac{17 π}{4}

Solve

\frac{2 x - π}{17} = \frac{3 π}{2} + 2 πn : x = 17 πn + \frac{π}{2} + \frac{51 π}{4}

\frac{2 x - π}{17} = \frac{3 π}{2} + 2 πn

Multiply both sides by

17

\frac{2 x - π}{17} = \frac{3 π}{2} + 2 πn

Multiply both sides by

17

\frac{17 ( 2 x - π )}{17} = 17 \cdot \frac{3 π}{2} + 17 \cdot 2 πn

Simplify

\frac{17 ( 2 x - π )}{17} = 17 \cdot \frac{3 π}{2} + 17 \cdot 2 πn

Simplify

\frac{17 ( 2 x - π )}{17} : 2 x - π

\frac{17 ( 2 x - π )}{17}

Divide the numbers:

\frac{17}{17} = 1

= 2 x - π

Simplify

17 \cdot \frac{3 π}{2} + 17 \cdot 2 πn : \frac{51 π}{2} + 34 πn

17 \cdot \frac{3 π}{2} + 17 \cdot 2 πn

17 \cdot \frac{3 π}{2} = \frac{51 π}{2}

17 \cdot \frac{3 π}{2}

Multiply fractions:

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

= \frac{3 π 17}{2}

Multiply the numbers:

3 \cdot 17 = 51

= \frac{51 π}{2}

17 \cdot 2 πn = 34 πn

17 \cdot 2 πn

Multiply the numbers:

17 \cdot 2 = 34

= 34 πn

= \frac{51 π}{2} + 34 πn

2 x - π = \frac{51 π}{2} + 34 πn

2 x - π = \frac{51 π}{2} + 34 πn

2 x - π = \frac{51 π}{2} + 34 πn

Move

π

to the right side

2 x - π = \frac{51 π}{2} + 34 πn

Add

π

to both sides

2 x - π + π = \frac{51 π}{2} + 34 πn + π

Simplify

2 x = \frac{51 π}{2} + 34 πn + π

2 x = \frac{51 π}{2} + 34 πn + π

Divide both sides by

2

2 x = \frac{51 π}{2} + 34 πn + π

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{51 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{51 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{51 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2} : 17 πn + \frac{π}{2} + \frac{51 π}{4}

\frac{\frac{51 π}{2}}{2} + \frac{34 πn}{2} + \frac{π}{2}

Group like terms

= \frac{π}{2} + \frac{34 πn}{2} + \frac{\frac{51 π}{2}}{2}

\frac{34 πn}{2} = 17 πn

\frac{34 πn}{2}

Divide the numbers:

\frac{34}{2} = 17

= 17 πn

\frac{\frac{51 π}{2}}{2} = \frac{51 π}{4}

\frac{\frac{51 π}{2}}{2}

Apply the fraction rule:

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

= \frac{51 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{51 π}{4}

= \frac{π}{2} + 17 πn + \frac{51 π}{4}

Group like terms

= 17 πn + \frac{π}{2} + \frac{51 π}{4}

x = 17 πn + \frac{π}{2} + \frac{51 π}{4}

x = 17 πn + \frac{π}{2} + \frac{51 π}{4}

x = 17 πn + \frac{π}{2} + \frac{51 π}{4}

x = 17 πn + \frac{π}{2} + \frac{17 π}{4}, x = 17 πn + \frac{π}{2} + \frac{51 π}{4}

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Frequently Asked Questions (FAQ)

What is the general solution for cos((2x-pi)/(17))=0 ?
The general solution for cos((2x-pi)/(17))=0 is x=17pin+pi/2+(17pi)/4 ,x=17pin+pi/2+(51pi)/4