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

The general solution for 4cot^2(θ)-9=0 is θ=0.58800…+pin,θ=2.55359…+pin

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Popular >

4cot^2(θ)-9=0

Solution

4 cot^{2} (θ) - 9 = 0

Solution

θ = 0.58800 \dots + πn, θ = 2.55359 \dots + πn

Degrees

θ = 33.69006 \dots^{\circ} + 18 0^{\circ} n, θ = 146.30993 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 cot^{2} (θ) - 9 = 0

Solve by substitution

4 cot^{2} (θ) - 9 = 0

Let:

cot (θ) = u

4 u^{2} - 9 = 0

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

4 u^{2} - 9 = 0

Move

9

to the right side

4 u^{2} - 9 = 0

Add

9

to both sides

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

Simplify

4 u^{2} = 9

4 u^{2} = 9

Divide both sides by

4

4 u^{2} = 9

Divide both sides by

4

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

Simplify

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

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

For

x^{2} = f (a)

the solutions are

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

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

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

\frac{9}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{9}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{9}{2}

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= \frac{3}{2}

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

- \frac{9}{4}

Simplify

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

\frac{9}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{9}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{9}{2}

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= \frac{3}{2}

= - \frac{3}{2}

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

Substitute back

u = cot (θ)

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

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

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

cot (θ) = \frac{3}{2}

Apply trig inverse properties

cot (θ) = \frac{3}{2}

General solutions for

cot (θ) = \frac{3}{2}

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

θ = arccot (\frac{3}{2}) + πn

θ = arccot (\frac{3}{2}) + πn

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

cot (θ) = - \frac{3}{2}

Apply trig inverse properties

cot (θ) = - \frac{3}{2}

General solutions for

cot (θ) = - \frac{3}{2}

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

θ = arccot (- \frac{3}{2}) + πn

θ = arccot (- \frac{3}{2}) + πn

Combine all the solutions

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

Show solutions in decimal form

θ = 0.58800 \dots + πn, θ = 2.55359 \dots + πn

Popular Examples

sin(x/2)=-(sqrt(3))/2

sin (\frac{x}{2}) = - \frac{3}{2}

2cos^3(x)=cos(x)

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

sqrt(3)sec(θ)+sec(θ)cot(θ)=0

3 sec (θ) + sec (θ) cot (θ) = 0

sqrt(3)tan(x/2)-1=0

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

cos(2x)=0.5

cos (2 x) = 0.5

Frequently Asked Questions (FAQ)

What is the general solution for 4cot^2(θ)-9=0 ?
The general solution for 4cot^2(θ)-9=0 is θ=0.58800…+pin,θ=2.55359…+pin