What is the general solution for cot^2(θ)=3,0<= x<= 2pi ?

The general solution for cot^2(θ)=3,0<= x<= 2pi is θ= pi/6 ,θ=(7pi)/6 ,θ=(5pi)/6 ,θ=(11pi)/6

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cot^2(θ)=3,0<= x<= 2pi

cot^{2} (θ) = 3, 0 \leq x \leq 2 π

θ = \frac{π}{6}, θ = \frac{7 π}{6}, θ = \frac{5 π}{6}, θ = \frac{11 π}{6}

Degrees

θ = 3 0^{\circ}, θ = 21 0^{\circ}, θ = 15 0^{\circ}, θ = 33 0^{\circ}

Solution steps

cot^{2} (θ) = 3, 0 \leq x \leq 2 π

Solve by substitution

cot^{2} (θ) = 3

Let:

cot (θ) = u

u^{2} = 3

u^{2} = 3 : u = 3, u = - 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 (θ)

cot (θ) = 3, cot (θ) = - 3

cot (θ) = 3, cot (θ) = - 3

cot (θ) = 3, 0 \leq x \leq 2 π : θ = \frac{π}{6}, θ = \frac{7 π}{6}

cot (θ) = 3, 0 \leq x \leq 2 π

General solutions for

cot (θ) = 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

θ = \frac{π}{6} + πn

θ = \frac{π}{6} + πn

Solutions for the range

0 \leq x \leq 2 π

θ = \frac{π}{6}, θ = \frac{7 π}{6}

cot (θ) = - 3, 0 \leq x \leq 2 π : θ = \frac{5 π}{6}, θ = \frac{11 π}{6}

cot (θ) = - 3, 0 \leq x \leq 2 π

General solutions for

cot (θ) = - 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

θ = \frac{5 π}{6} + πn

θ = \frac{5 π}{6} + πn

Solutions for the range

0 \leq x \leq 2 π

θ = \frac{5 π}{6}, θ = \frac{11 π}{6}

Combine all the solutions

θ = \frac{π}{6}, θ = \frac{7 π}{6}, θ = \frac{5 π}{6}, θ = \frac{11 π}{6}

tan (x) = \frac{14}{7}

2 (cos (x))^{2} - cos (x) - 1 = 0

0 = 5 + 4 cos (θ)

108 cos (0.5 a) = sin (9 0^{\circ} + a)

cos (x^{2} + 1) = 5

What is the general solution for cot^2(θ)=3,0<= x<= 2pi ?
The general solution for cot^2(θ)=3,0<= x<= 2pi is θ= pi/6 ,θ=(7pi)/6 ,θ=(5pi)/6 ,θ=(11pi)/6