What is the general solution for csc(θ)-1=0 ?

The general solution for csc(θ)-1=0 is θ= pi/2+2pin

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csc(θ)-1=0

csc (θ) - 1 = 0

θ = \frac{π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

csc (θ) - 1 = 0

Move

1

to the right side

csc (θ) - 1 = 0

Add

1

to both sides

csc (θ) - 1 + 1 = 0 + 1

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

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

2 sec^{2} (x) - 3 sec (x) - 2 = 0

tan (θ) + \frac{1}{3} = 0

12 cos^{2} (x) - 3 = 0

csc^{2} (θ) + 4 csc (θ) - 5 = 0

What is the general solution for csc(θ)-1=0 ?
The general solution for csc(θ)-1=0 is θ= pi/2+2pin