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

The general solution for -cot(2θ)=0 is θ= pi/4+(pin)/2

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-cot(2θ)=0

- cot (2 θ) = 0

θ = \frac{π}{4} + \frac{πn}{2}

Degrees

θ = 4 5^{\circ} + 9 0^{\circ} n

Solution steps

- cot (2 θ) = 0

Divide both sides by

- 1

- cot (2 θ) = 0

Divide both sides by

- 1

\frac{- cot ( 2 θ )}{- 1} = \frac{0}{- 1}

Simplify

cot (2 θ) = 0

cot (2 θ) = 0

General solutions for

cot (2 θ) = 0

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

2 θ = \frac{π}{2} + πn

2 θ = \frac{π}{2} + πn

Solve

2 θ = \frac{π}{2} + πn : θ = \frac{π}{4} + \frac{πn}{2}

2 θ = \frac{π}{2} + πn

Divide both sides by

2

2 θ = \frac{π}{2} + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{\frac{π}{2}}{2} + \frac{πn}{2}

Simplify

\frac{2 θ}{2} = \frac{\frac{π}{2}}{2} + \frac{πn}{2}

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

\frac{\frac{π}{2}}{2} + \frac{πn}{2} : \frac{π}{4} + \frac{πn}{2}

\frac{\frac{π}{2}}{2} + \frac{πn}{2}

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

= \frac{π}{4} + \frac{πn}{2}

θ = \frac{π}{4} + \frac{πn}{2}

θ = \frac{π}{4} + \frac{πn}{2}

θ = \frac{π}{4} + \frac{πn}{2}

θ = \frac{π}{4} + \frac{πn}{2}

1 - \frac{1}{2} \cdot cos (3 θ) = \frac{4 - 2}{4}, 0^{\circ} \leq θ \leq 36 0^{\circ}

\frac{cos ( x )}{sin ( x )} = - 0.00836

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

2 sin (θ) = 3 cos (θ) - 1, 0 <, θ < 360

cot (2 θ) + csc (2 θ) - 7 = 0

What is the general solution for -cot(2θ)=0 ?
The general solution for -cot(2θ)=0 is θ= pi/4+(pin)/2