What is the general solution for -cos(x-pi)=(sqrt(3))/2 ?

The general solution for -cos(x-pi)=(sqrt(3))/2 is x=(5pi)/6+2pin+pi,x=(7pi)/6+2pin+pi

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

Solution

- cos (x - π) = \frac{3}{2}

Solution

x = \frac{5 π}{6} + 2 πn + π, x = \frac{7 π}{6} + 2 πn + π

Degrees

x = 33 0^{\circ} + 36 0^{\circ} n, x = 39 0^{\circ} + 36 0^{\circ} n

Solution steps

- cos (x - π) = \frac{3}{2}

Divide both sides by

- 1

- cos (x - π) = \frac{3}{2}

Divide both sides by

- 1

\frac{- cos ( x - π )}{- 1} = \frac{\frac{3}{2}}{- 1}

Simplify

\frac{- cos ( x - π )}{- 1} = \frac{\frac{3}{2}}{- 1}

Simplify

\frac{- cos ( x - π )}{- 1} : cos (x - π)

\frac{- cos ( x - π )}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{cos ( x - π )}{1}

Apply rule

\frac{a}{1} = a

= cos (x - π)

Simplify

\frac{\frac{3}{2}}{- 1} : - \frac{3}{2}

\frac{\frac{3}{2}}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{3}{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{3}{2}}{1} = \frac{3}{2}

= - \frac{3}{2}

cos (x - π) = - \frac{3}{2}

cos (x - π) = - \frac{3}{2}

cos (x - π) = - \frac{3}{2}

General solutions for

cos (x - π) = - \frac{3}{2}

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}

x - π = \frac{5 π}{6} + 2 πn, x - π = \frac{7 π}{6} + 2 πn

x - π = \frac{5 π}{6} + 2 πn, x - π = \frac{7 π}{6} + 2 πn

Solve

x - π = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{6} + 2 πn + π

x - π = \frac{5 π}{6} + 2 πn

Move

π

to the right side

x - π = \frac{5 π}{6} + 2 πn

Add

π

to both sides

x - π + π = \frac{5 π}{6} + 2 πn + π

Simplify

x = \frac{5 π}{6} + 2 πn + π

x = \frac{5 π}{6} + 2 πn + π

Solve

x - π = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{6} + 2 πn + π

x - π = \frac{7 π}{6} + 2 πn

Move

π

to the right side

x - π = \frac{7 π}{6} + 2 πn

Add

π

to both sides

x - π + π = \frac{7 π}{6} + 2 πn + π

Simplify

x = \frac{7 π}{6} + 2 πn + π

x = \frac{7 π}{6} + 2 πn + π

x = \frac{5 π}{6} + 2 πn + π, x = \frac{7 π}{6} + 2 πn + π

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sin^{2} (x + \frac{π}{2}) = \frac{3}{4}

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2 cos (x) + 1 = 3 sec (x)

csc(θ)= 5/4

csc (θ) = \frac{5}{4}

Frequently Asked Questions (FAQ)

What is the general solution for -cos(x-pi)=(sqrt(3))/2 ?
The general solution for -cos(x-pi)=(sqrt(3))/2 is x=(5pi)/6+2pin+pi,x=(7pi)/6+2pin+pi