What is the general solution for 4csc(θ)+4=0 ?

The general solution for 4csc(θ)+4=0 is θ=(3pi)/2+2pin

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4csc(θ)+4=0

4 csc (θ) + 4 = 0

θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

4 csc (θ) + 4 = 0

Move

4

to the right side

4 csc (θ) + 4 = 0

Subtract

4

from both sides

4 csc (θ) + 4 - 4 = 0 - 4

Simplify

4 csc (θ) = - 4

4 csc (θ) = - 4

Divide both sides by

4

4 csc (θ) = - 4

Divide both sides by

4

\frac{4 csc ( θ )}{4} = \frac{- 4}{4}

Simplify

csc (θ) = - 1

csc (θ) = - 1

General solutions for

csc (θ) = - 1

csc (x)

periodicity table with

2 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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

θ = \frac{3 π}{2} + 2 πn

θ = \frac{3 π}{2} + 2 πn

tan (a) = \frac{7}{8}

\frac{sec ( x ) sin ( x )}{tan ( x ) cot ( x )} = sin^{2} (x)

sin (3 x) + cos (3 x) = 0

sin (x) = - \frac{3}{4}, π < x < \frac{3 π}{4}

cos (2 x) + cos (x) = 0, 0 \leq x < 2 π

What is the general solution for 4csc(θ)+4=0 ?
The general solution for 4csc(θ)+4=0 is θ=(3pi)/2+2pin