What is the general solution for csc(a)=3 ?

The general solution for csc(a)=3 is a=0.33983…+2pin,a=pi-0.33983…+2pin

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csc(a)=3

csc (a) = 3

a = 0.33983 \dots + 2 πn, a = π - 0.33983 \dots + 2 πn

Degrees

a = 19.47122 \dots^{\circ} + 36 0^{\circ} n, a = 160.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

csc (a) = 3

Apply trig inverse properties

csc (a) = 3

General solutions for

csc (a) = 3

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

a = arccsc (3) + 2 πn, a = π - arccsc (3) + 2 πn

a = arccsc (3) + 2 πn, a = π - arccsc (3) + 2 πn

Show solutions in decimal form

a = 0.33983 \dots + 2 πn, a = π - 0.33983 \dots + 2 πn

csc (a) = 5

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)

What is the general solution for csc(a)=3 ?
The general solution for csc(a)=3 is a=0.33983…+2pin,a=pi-0.33983…+2pin