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

The general solution for 4cot(θ)-1=0 is θ=1.32581…+pin

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4cot(θ)-1=0

4 cot (θ) - 1 = 0

θ = 1.32581 \dots + πn

Degrees

θ = 75.96375 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 cot (θ) - 1 = 0

Move

1

to the right side

4 cot (θ) - 1 = 0

Add

1

to both sides

4 cot (θ) - 1 + 1 = 0 + 1

Simplify

4 cot (θ) = 1

4 cot (θ) = 1

Divide both sides by

4

4 cot (θ) = 1

Divide both sides by

4

\frac{4 cot ( θ )}{4} = \frac{1}{4}

Simplify

cot (θ) = \frac{1}{4}

cot (θ) = \frac{1}{4}

Apply trig inverse properties

cot (θ) = \frac{1}{4}

General solutions for

cot (θ) = \frac{1}{4}

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

θ = arccot (\frac{1}{4}) + πn

θ = arccot (\frac{1}{4}) + πn

Show solutions in decimal form

θ = 1.32581 \dots + πn

x, 4 cos^{2} (x) = 5 - 4 sin (x)

cos (x) = \frac{2}{3}, - \frac{5 π}{2} < x < 2 π

\frac{3 sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )} = 4

\frac{1}{e ^{s i n (x)}} = 1

∣ cos (x) ∣ = \frac{3}{2}

What is the general solution for 4cot(θ)-1=0 ?
The general solution for 4cot(θ)-1=0 is θ=1.32581…+pin