What is the general solution for 9cot^2(θ)-4=0 ?

The general solution for 9cot^2(θ)-4=0 is θ=0.98279…+pin,θ=2.15879…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9cot^2(θ)-4=0

Solution

9 cot^{2} (θ) - 4 = 0

Solution

θ = 0.98279 \dots + πn, θ = 2.15879 \dots + πn

Degrees

θ = 56.30993 \dots^{\circ} + 18 0^{\circ} n, θ = 123.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

9 cot^{2} (θ) - 4 = 0

Solve by substitution

9 cot^{2} (θ) - 4 = 0

Let:

cot (θ) = u

9 u^{2} - 4 = 0

9 u^{2} - 4 = 0 : u = \frac{2}{3}, u = - \frac{2}{3}

9 u^{2} - 4 = 0

Move

4

to the right side

9 u^{2} - 4 = 0

Add

4

to both sides

9 u^{2} - 4 + 4 = 0 + 4

Simplify

9 u^{2} = 4

9 u^{2} = 4

Divide both sides by

9

9 u^{2} = 4

Divide both sides by

9

\frac{9 u ^{2}}{9} = \frac{4}{9}

Simplify

u^{2} = \frac{4}{9}

u^{2} = \frac{4}{9}

For

x^{2} = f (a)

the solutions are

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

u = \frac{4}{9}, u = - \frac{4}{9}

\frac{4}{9} = \frac{2}{3}

\frac{4}{9}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4}{9}

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= \frac{4}{3}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{2}{3}

- \frac{4}{9} = - \frac{2}{3}

- \frac{4}{9}

Simplify

\frac{4}{9} : \frac{2}{3}

\frac{4}{9}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4}{9}

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= \frac{4}{3}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{2}{3}

= - \frac{2}{3}

u = \frac{2}{3}, u = - \frac{2}{3}

Substitute back

u = cot (θ)

cot (θ) = \frac{2}{3}, cot (θ) = - \frac{2}{3}

cot (θ) = \frac{2}{3}, cot (θ) = - \frac{2}{3}

cot (θ) = \frac{2}{3} : θ = arccot (\frac{2}{3}) + πn

cot (θ) = \frac{2}{3}

Apply trig inverse properties

cot (θ) = \frac{2}{3}

General solutions for

cot (θ) = \frac{2}{3}

cot (x) = a \Rightarrow x = arccot (a) + πn

θ = arccot (\frac{2}{3}) + πn

θ = arccot (\frac{2}{3}) + πn

cot (θ) = - \frac{2}{3} : θ = arccot (- \frac{2}{3}) + πn

cot (θ) = - \frac{2}{3}

Apply trig inverse properties

cot (θ) = - \frac{2}{3}

General solutions for

cot (θ) = - \frac{2}{3}

cot (x) = - a \Rightarrow x = arccot (- a) + πn

θ = arccot (- \frac{2}{3}) + πn

θ = arccot (- \frac{2}{3}) + πn

Combine all the solutions

θ = arccot (\frac{2}{3}) + πn, θ = arccot (- \frac{2}{3}) + πn

Show solutions in decimal form

θ = 0.98279 \dots + πn, θ = 2.15879 \dots + πn

Popular Examples

4sin^2(θ)=1+4cos(θ)

4 sin^{2} (θ) = 1 + 4 cos (θ)

4sin(θ)+1=2sin(θ)

4 sin (θ) + 1 = 2 sin (θ)

cot(θ)= 1/2

cot (θ) = \frac{1}{2}

sin(θ)=0.7

sin (θ) = 0.7

sin(θ)=0.2

sin (θ) = 0.2

Frequently Asked Questions (FAQ)

What is the general solution for 9cot^2(θ)-4=0 ?
The general solution for 9cot^2(θ)-4=0 is θ=0.98279…+pin,θ=2.15879…+pin