What is the general solution for 4sec(x)+8=0,0<= x<= 360 ?

The general solution for 4sec(x)+8=0,0<= x<= 360 is x=120,x=240

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4sec(x)+8=0,0<= x<= 360

4 sec (x) + 8 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

x = 12 0^{\circ}, x = 24 0^{\circ}

Radians

x = \frac{2 π}{3}, x = \frac{4 π}{3}

Solution steps

4 sec (x) + 8 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

Move

8

to the right side

4 sec (x) + 8 = 0

Subtract

8

from both sides

4 sec (x) + 8 - 8 = 0 - 8

Simplify

4 sec (x) = - 8

4 sec (x) = - 8

Divide both sides by

4

4 sec (x) = - 8

Divide both sides by

4

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

Simplify

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

Simplify

\frac{4 sec ( x )}{4} : sec (x)

\frac{4 sec ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sec (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 (x) = - 2

sec (x) = - 2

sec (x) = - 2

General solutions for

sec (x) = - 2

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solutions for the range

0 \leq x \leq 36 0^{\circ}

x = 12 0^{\circ}, x = 24 0^{\circ}

What is the general solution for 4sec(x)+8=0,0<= x<= 360 ?
The general solution for 4sec(x)+8=0,0<= x<= 360 is x=120,x=240