What is the general solution for 5csc(θ)-3=2 ?

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

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5csc(θ)-3=2

5 csc (θ) - 3 = 2

θ = \frac{π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

5 csc (θ) - 3 = 2

Move

3

to the right side

5 csc (θ) - 3 = 2

Add

3

to both sides

5 csc (θ) - 3 + 3 = 2 + 3

Simplify

5 csc (θ) = 5

5 csc (θ) = 5

Divide both sides by

5

5 csc (θ) = 5

Divide both sides by

5

\frac{5 csc ( θ )}{5} = \frac{5}{5}

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{π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn

3 cos (θ - 5 5^{\circ}) = - 1.56

cot (3 x) = 3

sin (2 θ) - sin (θ) = 0

- 4 sin (4 x) = 0

cos (x) = - 3

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