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

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

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Popular >

sec(-2x)=-2

Solution

sec (- 2 x) = - 2

Solution

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

Degrees

x = - 6 0^{\circ} - 18 0^{\circ} n, x = - 12 0^{\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{2 π}{3} + 2 πn, - 2 x = \frac{4 π}{3} + 2 πn

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

Solve

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

- 2 x = \frac{2 π}{3} + 2 πn

Divide both sides by

- 2

- 2 x = \frac{2 π}{3} + 2 πn

Divide both sides by

- 2

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

Simplify

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

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

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

\frac{\frac{2 π}{3}}{- 2}

Apply the fraction rule:

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

= - \frac{\frac{2 π}{3}}{2}

Apply the fraction rule:

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

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

= - \frac{2 π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= - \frac{2 π}{6}

Cancel the common factor:

2

= - \frac{π}{3}

= - \frac{π}{3} + \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{π}{3} - πn

x = - \frac{π}{3} - πn

x = - \frac{π}{3} - πn

x = - \frac{π}{3} - πn

Solve

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

- 2 x = \frac{4 π}{3} + 2 πn

Divide both sides by

- 2

- 2 x = \frac{4 π}{3} + 2 πn

Divide both sides by

- 2

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

Simplify

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

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

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

\frac{\frac{4 π}{3}}{- 2}

Apply the fraction rule:

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

= - \frac{\frac{4 π}{3}}{2}

Apply the fraction rule:

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

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

= - \frac{4 π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= - \frac{4 π}{6}

Cancel the common factor:

2

= - \frac{2 π}{3}

= - \frac{2 π}{3} + \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{2 π}{3} - πn

x = - \frac{2 π}{3} - πn

x = - \frac{2 π}{3} - πn

x = - \frac{2 π}{3} - πn

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

Popular Examples

tan(θ/2-pi/3)=1

tan (\frac{θ}{2} - \frac{π}{3}) = 1

sinh(x)= 3/4

sinh (x) = \frac{3}{4}

sin(θ)=2sin(θ)+1

sin (θ) = 2 sin (θ) + 1

8sin(x)tan(x)=-7tan(x)

8 sin (x) tan (x) = - 7 tan (x)

cos(x)= 8/17

cos (x) = \frac{8}{17}

Frequently Asked Questions (FAQ)

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