What is the general solution for 0= 1/3*cot(-4θ) ?

The general solution for 0= 1/3*cot(-4θ) is θ=-pi/8-(pin)/4

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0= 1/3*cot(-4θ)

0 = \frac{1}{3} \cdot cot (- 4 θ)

θ = - \frac{π}{8} - \frac{πn}{4}

Degrees

θ = - 22. 5^{\circ} - 4 5^{\circ} n

Solution steps

0 = \frac{1}{3} cot (- 4 θ)

Switch sides

\frac{1}{3} cot (- 4 θ) = 0

Multiply both sides by

3

\frac{1}{3} cot (- 4 θ) = 0

Multiply both sides by

3

3 \cdot \frac{1}{3} cot (- 4 θ) = 0 \cdot 3

Simplify

cot (- 4 θ) = 0

cot (- 4 θ) = 0

General solutions for

cot (- 4 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

- 4 θ = \frac{π}{2} + πn

- 4 θ = \frac{π}{2} + πn

Solve

- 4 θ = \frac{π}{2} + πn : θ = - \frac{π}{8} - \frac{πn}{4}

- 4 θ = \frac{π}{2} + πn

Divide both sides by

- 4

- 4 θ = \frac{π}{2} + πn

Divide both sides by

- 4

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

Simplify

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

Simplify

\frac{- 4 θ}{- 4} : θ

\frac{- 4 θ}{- 4}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

\frac{\frac{π}{2}}{- 4} + \frac{πn}{- 4} : - \frac{π}{8} - \frac{πn}{4}

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

\frac{\frac{π}{2}}{- 4} = - \frac{π}{8}

\frac{\frac{π}{2}}{- 4}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{π}{2}}{4}

Apply the fraction rule:

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

\frac{\frac{π}{2}}{4} = \frac{π}{2 \cdot 4}

= - \frac{π}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= - \frac{π}{8}

= - \frac{π}{8} + \frac{πn}{- 4}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{π}{8} - \frac{πn}{4}

θ = - \frac{π}{8} - \frac{πn}{4}

θ = - \frac{π}{8} - \frac{πn}{4}

θ = - \frac{π}{8} - \frac{πn}{4}

θ = - \frac{π}{8} - \frac{πn}{4}

\frac{62 5 ^{c o s^{2} (x)}}{2 5 ^{c o s (x)}} = 1

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

2 cos (x) - 3 sec (x) = 5

cos (2 x) = 1 - 2 sin (x), 0 \leq x < 2 π

5 tan (x) = 53

What is the general solution for 0= 1/3*cot(-4θ) ?
The general solution for 0= 1/3*cot(-4θ) is θ=-pi/8-(pin)/4