What is the general solution for 3cot(θ)-8=-11 ?

The general solution for 3cot(θ)-8=-11 is θ=(3pi)/4+pin

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3cot(θ)-8=-11

3 cot (θ) - 8 = - 11

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

3 cot (θ) - 8 = - 11

Move

8

to the right side

3 cot (θ) - 8 = - 11

Add

8

to both sides

3 cot (θ) - 8 + 8 = - 11 + 8

Simplify

3 cot (θ) = - 3

3 cot (θ) = - 3

Divide both sides by

3

3 cot (θ) = - 3

Divide both sides by

3

\frac{3 cot ( θ )}{3} = \frac{- 3}{3}

Simplify

cot (θ) = - 1

cot (θ) = - 1

General solutions for

cot (θ) = - 1

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{3 π}{4} + πn

θ = \frac{3 π}{4} + πn

2 cos (\frac{π}{4} - x) = 1

sin (θ) = \frac{56}{65}

900 = 400 sin (\frac{2 π t}{365} + \frac{7 π}{8}) + 500

2 sin^{2} (x) + 2 sin (x) = 0

2 sin^{2} (x) = sin (x) + 1, 0 \leq x \leq 2 π

What is the general solution for 3cot(θ)-8=-11 ?
The general solution for 3cot(θ)-8=-11 is θ=(3pi)/4+pin