What is the general solution for csc(a)=5 ?

The general solution for csc(a)=5 is a=0.20135…+2pin,a=pi-0.20135…+2pin

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csc(a)=5

csc (a) = 5

a = 0.20135 \dots + 2 πn, a = π - 0.20135 \dots + 2 πn

Degrees

a = 11.53695 \dots^{\circ} + 36 0^{\circ} n, a = 168.46304 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (a) = 5

Apply trig inverse properties

csc (a) = 5

General solutions for

csc (a) = 5

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

a = arccsc (5) + 2 πn, a = π - arccsc (5) + 2 πn

a = arccsc (5) + 2 πn, a = π - arccsc (5) + 2 πn

Show solutions in decimal form

a = 0.20135 \dots + 2 πn, a = π - 0.20135 \dots + 2 πn

1 - \frac{1}{2} cos (2 x - \frac{π}{2}) = 0

sin (π x) = - sin (π - π x)

sin (x) cos (x) = 2 sin (x)

2 + 2 cos (θ) = 2 - 2 sin (θ)

sin (b) = 0.7245

What is the general solution for csc(a)=5 ?
The general solution for csc(a)=5 is a=0.20135…+2pin,a=pi-0.20135…+2pin