What is the general solution for 4csc(θ)-5=3 ?

The general solution for 4csc(θ)-5=3 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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4csc(θ)-5=3

4 csc (θ) - 5 = 3

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

4 csc (θ) - 5 = 3

Move

5

to the right side

4 csc (θ) - 5 = 3

Add

5

to both sides

4 csc (θ) - 5 + 5 = 3 + 5

Simplify

4 csc (θ) = 8

4 csc (θ) = 8

Divide both sides by

4

4 csc (θ) = 8

Divide both sides by

4

\frac{4 csc ( θ )}{4} = \frac{8}{4}

Simplify

csc (θ) = 2

csc (θ) = 2

General solutions for

csc (θ) = 2

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{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

csc (5 x) = - 1, 0 \leq x \leq 2 π

- 4 \cdot cos^{2} (x) + 3 = 0

8 sin (θ) + 1 = 6 sin (θ)

- cot^{2} (x) = 1 + 2 cot (x)

6 sec (2 x) + 3 tan (2 x) - 9 = 0

What is the general solution for 4csc(θ)-5=3 ?
The general solution for 4csc(θ)-5=3 is θ= pi/6+2pin,θ=(5pi)/6+2pin