What is the general solution for cos(9x)=-1 ?

The general solution for cos(9x)=-1 is x= pi/9+(2pin)/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(9x)=-1

cos (9 x) = - 1

x = \frac{π}{9} + \frac{2 πn}{9}

Degrees

x = 2 0^{\circ} + 4 0^{\circ} n

Solution steps

cos (9 x) = - 1

General solutions for

cos (9 x) = - 1

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

9 x = π + 2 πn

9 x = π + 2 πn

Solve

9 x = π + 2 πn : x = \frac{π}{9} + \frac{2 πn}{9}

9 x = π + 2 πn

Divide both sides by

9

9 x = π + 2 πn

Divide both sides by

9

\frac{9 x}{9} = \frac{π}{9} + \frac{2 πn}{9}

Simplify

x = \frac{π}{9} + \frac{2 πn}{9}

x = \frac{π}{9} + \frac{2 πn}{9}

x = \frac{π}{9} + \frac{2 πn}{9}

tan^{2} (θ) = 3, 0 \leq θ \leq 2 π

3 sin (x) - 2 cos^{2} (x) = 0

4 cos^{2} (x) + 4 cos (x) - 3 = 0

sin (4 x) cos (x) - cos (4 x) sin (x) = 0

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

What is the general solution for cos(9x)=-1 ?
The general solution for cos(9x)=-1 is x= pi/9+(2pin)/9