What is the general solution for 4sec(pix)+6=-2 ?

The general solution for 4sec(pix)+6=-2 is x= 2/3+2n,x= 4/3+2n

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4sec(pix)+6=-2

Solution

4 sec (π x) + 6 = - 2

Solution

x = \frac{2}{3} + 2 n, x = \frac{4}{3} + 2 n

Degrees

x = 38.19718 \dots^{\circ} + 114.59155 \dots^{\circ} n, x = 76.39437 \dots^{\circ} + 114.59155 \dots^{\circ} n

Solution steps

4 sec (π x) + 6 = - 2

Move

6

to the right side

4 sec (π x) + 6 = - 2

Subtract

6

from both sides

4 sec (π x) + 6 - 6 = - 2 - 6

Simplify

4 sec (π x) = - 8

4 sec (π x) = - 8

Divide both sides by

4

4 sec (π x) = - 8

Divide both sides by

4

\frac{4 sec ( π x )}{4} = \frac{- 8}{4}

Simplify

\frac{4 sec ( π x )}{4} = \frac{- 8}{4}

Simplify

\frac{4 sec ( π x )}{4} : sec (π x)

\frac{4 sec ( π x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sec (π x)

Simplify

\frac{- 8}{4} : - 2

\frac{- 8}{4}

Apply the fraction rule:

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

= - \frac{8}{4}

Divide the numbers:

\frac{8}{4} = 2

= - 2

sec (π x) = - 2

sec (π x) = - 2

sec (π x) = - 2

General solutions for

sec (π x) = - 2

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

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

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

Solve

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

π x = \frac{2 π}{3} + 2 πn

Divide both sides by

π

π x = \frac{2 π}{3} + 2 πn

Divide both sides by

π

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

Simplify

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

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{\frac{2 π}{3}}{π} + \frac{2 πn}{π} : \frac{2}{3} + 2 n

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

\frac{\frac{2 π}{3}}{π} = \frac{2}{3}

\frac{\frac{2 π}{3}}{π}

Apply the fraction rule:

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

= \frac{2 π}{3 π}

Cancel the common factor:

π

= \frac{2}{3}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

Cancel the common factor:

π

= 2 n

= \frac{2}{3} + 2 n

x = \frac{2}{3} + 2 n

x = \frac{2}{3} + 2 n

x = \frac{2}{3} + 2 n

Solve

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

π x = \frac{4 π}{3} + 2 πn

Divide both sides by

π

π x = \frac{4 π}{3} + 2 πn

Divide both sides by

π

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

Simplify

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

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

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

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

\frac{\frac{4 π}{3}}{π} = \frac{4}{3}

\frac{\frac{4 π}{3}}{π}

Apply the fraction rule:

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

= \frac{4 π}{3 π}

Cancel the common factor:

π

= \frac{4}{3}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

Cancel the common factor:

π

= 2 n

= \frac{4}{3} + 2 n

x = \frac{4}{3} + 2 n

x = \frac{4}{3} + 2 n

x = \frac{4}{3} + 2 n

x = \frac{2}{3} + 2 n, x = \frac{4}{3} + 2 n

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Frequently Asked Questions (FAQ)

What is the general solution for 4sec(pix)+6=-2 ?
The general solution for 4sec(pix)+6=-2 is x= 2/3+2n,x= 4/3+2n