What is the general solution for 3cot^2(x)=9 ?

The general solution for 3cot^2(x)=9 is x= pi/6+pin,x=(5pi)/6+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3cot^2(x)=9

3 cot^{2} (x) = 9

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Degrees

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

3 cot^{2} (x) = 9

Solve by substitution

3 cot^{2} (x) = 9

Let:

cot (x) = u

3 u^{2} = 9

3 u^{2} = 9 : u = 3, u = - 3

3 u^{2} = 9

Divide both sides by

3

3 u^{2} = 9

Divide both sides by

3

\frac{3 u ^{2}}{3} = \frac{9}{3}

Simplify

u^{2} = 3

u^{2} = 3

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 3, u = - 3

Substitute back

u = cot (x)

cot (x) = 3, cot (x) = - 3

cot (x) = 3, cot (x) = - 3

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = 3

General solutions for

cot (x) = 3

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

cot (x) = - 3 : x = \frac{5 π}{6} + πn

cot (x) = - 3

General solutions for

cot (x) = - 3

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

1 2^{(2)} = 1 3^{(2)} + 5^{(2)} - 2 (13) (5) cos (B)

tan (6 t) = 2

sin (2 x) - sin (x) + cos (2 x) + cos (x) = 0

(cos (x) = 1) = (sec (x) = 1)

cot (\frac{x}{3}) = \frac{- 1}{3}

What is the general solution for 3cot^2(x)=9 ?
The general solution for 3cot^2(x)=9 is x= pi/6+pin,x=(5pi)/6+pin