What is the general solution for sec(-2x)=-sqrt(2) ?

The general solution for sec(-2x)=-sqrt(2) is x=-(3pi)/8-pin,x=-(5pi)/8-pin

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sec(-2x)=-sqrt(2)

Solution

sec (- 2 x) = - 2

Solution

x = - \frac{3 π}{8} - πn, x = - \frac{5 π}{8} - πn

Degrees

x = - 67. 5^{\circ} - 18 0^{\circ} n, x = - 112. 5^{\circ} - 18 0^{\circ} n

Solution steps

sec (- 2 x) = - 2

General solutions for

sec (- 2 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}

- 2 x = \frac{3 π}{4} + 2 πn, - 2 x = \frac{5 π}{4} + 2 πn

- 2 x = \frac{3 π}{4} + 2 πn, - 2 x = \frac{5 π}{4} + 2 πn

Solve

- 2 x = \frac{3 π}{4} + 2 πn : x = - \frac{3 π}{8} - πn

- 2 x = \frac{3 π}{4} + 2 πn

Divide both sides by

- 2

- 2 x = \frac{3 π}{4} + 2 πn

Divide both sides by

- 2

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

Simplify

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

Simplify

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

Apply the fraction rule:

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

= \frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{3 π}{4}}{- 2} + \frac{2 πn}{- 2} : - \frac{3 π}{8} - πn

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

\frac{\frac{3 π}{4}}{- 2} = - \frac{3 π}{8}

\frac{\frac{3 π}{4}}{- 2}

Apply the fraction rule:

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

= - \frac{\frac{3 π}{4}}{2}

Apply the fraction rule:

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

\frac{\frac{3 π}{4}}{2} = \frac{3 π}{4 \cdot 2}

= - \frac{3 π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= - \frac{3 π}{8}

= - \frac{3 π}{8} + \frac{2 πn}{- 2}

\frac{2 πn}{- 2} = - πn

\frac{2 πn}{- 2}

Apply the fraction rule:

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

= - \frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= - πn

= - \frac{3 π}{8} - πn

x = - \frac{3 π}{8} - πn

x = - \frac{3 π}{8} - πn

x = - \frac{3 π}{8} - πn

Solve

- 2 x = \frac{5 π}{4} + 2 πn : x = - \frac{5 π}{8} - πn

- 2 x = \frac{5 π}{4} + 2 πn

Divide both sides by

- 2

- 2 x = \frac{5 π}{4} + 2 πn

Divide both sides by

- 2

\frac{- 2 x}{- 2} = \frac{\frac{5 π}{4}}{- 2} + \frac{2 πn}{- 2}

Simplify

\frac{- 2 x}{- 2} = \frac{\frac{5 π}{4}}{- 2} + \frac{2 πn}{- 2}

Simplify

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

Apply the fraction rule:

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

= \frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{5 π}{4}}{- 2} + \frac{2 πn}{- 2} : - \frac{5 π}{8} - πn

\frac{\frac{5 π}{4}}{- 2} + \frac{2 πn}{- 2}

\frac{\frac{5 π}{4}}{- 2} = - \frac{5 π}{8}

\frac{\frac{5 π}{4}}{- 2}

Apply the fraction rule:

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

= - \frac{\frac{5 π}{4}}{2}

Apply the fraction rule:

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

\frac{\frac{5 π}{4}}{2} = \frac{5 π}{4 \cdot 2}

= - \frac{5 π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= - \frac{5 π}{8}

= - \frac{5 π}{8} + \frac{2 πn}{- 2}

\frac{2 πn}{- 2} = - πn

\frac{2 πn}{- 2}

Apply the fraction rule:

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

= - \frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= - πn

= - \frac{5 π}{8} - πn

x = - \frac{5 π}{8} - πn

x = - \frac{5 π}{8} - πn

x = - \frac{5 π}{8} - πn

x = - \frac{3 π}{8} - πn, x = - \frac{5 π}{8} - πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sec(-2x)=-sqrt(2) ?
The general solution for sec(-2x)=-sqrt(2) is x=-(3pi)/8-pin,x=-(5pi)/8-pin