What is the general solution for sec(3x)=-sqrt(2) ?

The general solution for sec(3x)=-sqrt(2) is x= pi/4+(2pin)/3 ,x=(5pi}{12}+\frac{2pin)/3

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sec(3x)=-sqrt(2)

Solution

sec (3 x) = - 2

Solution

x = \frac{π}{4} + \frac{2 πn}{3}, x = \frac{5 π}{12} + \frac{2 πn}{3}

Degrees

x = 4 5^{\circ} + 12 0^{\circ} n, x = 7 5^{\circ} + 12 0^{\circ} n

Solution steps

sec (3 x) = - 2

General solutions for

sec (3 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}

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

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

Solve

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

3 x = \frac{3 π}{4} + 2 πn

Divide both sides by

3

3 x = \frac{3 π}{4} + 2 πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

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

\frac{\frac{3 π}{4}}{3} = \frac{π}{4}

\frac{\frac{3 π}{4}}{3}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{3 π}{12}

Cancel the common factor:

3

= \frac{π}{4}

= \frac{π}{4} + \frac{2 πn}{3}

x = \frac{π}{4} + \frac{2 πn}{3}

x = \frac{π}{4} + \frac{2 πn}{3}

x = \frac{π}{4} + \frac{2 πn}{3}

Solve

3 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{12} + \frac{2 πn}{3}

3 x = \frac{5 π}{4} + 2 πn

Divide both sides by

3

3 x = \frac{5 π}{4} + 2 πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{5 π}{4}}{3} + \frac{2 πn}{3} : \frac{5 π}{12} + \frac{2 πn}{3}

\frac{\frac{5 π}{4}}{3} + \frac{2 πn}{3}

\frac{\frac{5 π}{4}}{3} = \frac{5 π}{12}

\frac{\frac{5 π}{4}}{3}

Apply the fraction rule:

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

= \frac{5 π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{5 π}{12}

= \frac{5 π}{12} + \frac{2 πn}{3}

x = \frac{5 π}{12} + \frac{2 πn}{3}

x = \frac{5 π}{12} + \frac{2 πn}{3}

x = \frac{5 π}{12} + \frac{2 πn}{3}

x = \frac{π}{4} + \frac{2 πn}{3}, x = \frac{5 π}{12} + \frac{2 πn}{3}

Popular Examples

8cos(θ)=2sec(θ)

8 cos (θ) = 2 sec (θ)

2sin(x)-csc(x)=0

2 sin (x) - csc (x) = 0

sin(x)+sqrt(sin(x))=0

sin (x) + sin (x) = 0

3sec(x)-5=0

3 sec (x) - 5 = 0

5cos(θ)-5=0

5 cos (θ) - 5 = 0

Frequently Asked Questions (FAQ)

What is the general solution for sec(3x)=-sqrt(2) ?
The general solution for sec(3x)=-sqrt(2) is x= pi/4+(2pin)/3 ,x=(5pi}{12}+\frac{2pin)/3