What is the general solution for 9+cot^2(x)=12 ?

The general solution for 9+cot^2(x)=12 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 >

9+cot^2(x)=12

9 + cot^{2} (x) = 12

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

9 + cot^{2} (x) = 12

Solve by substitution

9 + cot^{2} (x) = 12

Let:

cot (x) = u

9 + u^{2} = 12

9 + u^{2} = 12 : u = 3, u = - 3

9 + u^{2} = 12

Move

9

to the right side

9 + u^{2} = 12

Subtract

9

from both sides

9 + u^{2} - 9 = 12 - 9

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

cos (a) = 0.8

cos (a) = 0.6

5 cos^{2} (θ) = 6 sin (θ)

8 tan (θ) = 0

12 cos^{2} (x) + 11 cos (x) - 5 = 0

What is the general solution for 9+cot^2(x)=12 ?
The general solution for 9+cot^2(x)=12 is x= pi/6+pin,x=(5pi)/6+pin