What is the general solution for sec(3x)=-1 ?

The general solution for sec(3x)=-1 is x= pi/3+(2pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(3x)=-1

sec (3 x) = - 1

x = \frac{π}{3} + \frac{2 πn}{3}

Degrees

x = 6 0^{\circ} + 12 0^{\circ} n

Solution steps

sec (3 x) = - 1

General solutions for

sec (3 x) = - 1

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 = π + 2 πn

3 x = π + 2 πn

Solve

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

3 x = π + 2 πn

Divide both sides by

3

3 x = π + 2 πn

Divide both sides by

3

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

Simplify

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

2 cos^{2} (x) + 1 = 3 cos (x)

cos (x) + 2 = 3 cos (x)

tan (2 θ) = 0

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

sin (\frac{θ}{2}) = - \frac{3}{2}

What is the general solution for sec(3x)=-1 ?
The general solution for sec(3x)=-1 is x= pi/3+(2pin)/3