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

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

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cot(θ)+1=0

cot (θ) + 1 = 0

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

cot (θ) + 1 = 0

Move

1

to the right side

cot (θ) + 1 = 0

Subtract

1

from both sides

cot (θ) + 1 - 1 = 0 - 1

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 sin^{2} (θ) - sin (θ) - 1 = 0

tan (7 5^{\circ})

cos (21 0^{\circ})

cos^{2} (x) = 2 - 2 sin (x)

cos (2 π)

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