What is the general solution for 5sec(x)+7=-3 ?

The general solution for 5sec(x)+7=-3 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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5sec(x)+7=-3

5 sec (x) + 7 = - 3

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

Degrees

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

Solution steps

5 sec (x) + 7 = - 3

Move

7

to the right side

5 sec (x) + 7 = - 3

Subtract

7

from both sides

5 sec (x) + 7 - 7 = - 3 - 7

Simplify

5 sec (x) = - 10

5 sec (x) = - 10

Divide both sides by

5

5 sec (x) = - 10

Divide both sides by

5

\frac{5 sec ( x )}{5} = \frac{- 10}{5}

Simplify

\frac{5 sec ( x )}{5} = \frac{- 10}{5}

Simplify

\frac{5 sec ( x )}{5} : sec (x)

\frac{5 sec ( x )}{5}

Divide the numbers:

\frac{5}{5} = 1

= sec (x)

Simplify

\frac{- 10}{5} : - 2

\frac{- 10}{5}

Apply the fraction rule:

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

= - \frac{10}{5}

Divide the numbers:

\frac{10}{5} = 2

= - 2

sec (x) = - 2

sec (x) = - 2

sec (x) = - 2

General solutions for

sec (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}

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

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

cos (2 θ) + 2 cos (θ) = - 1

(\frac{tan ( x )}{1})^{- 1} = \frac{20}{9.7}

1 - tan (x) = sec (x)

sec (\frac{3 θ}{2}) = - 2, 0 \leq θ < 2 π

tan (x - \frac{π}{6}) = 3

What is the general solution for 5sec(x)+7=-3 ?
The general solution for 5sec(x)+7=-3 is x=(2pi)/3+2pin,x=(4pi)/3+2pin