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

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

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csc(x)=-5

csc (x) = - 5

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

Solution steps

csc (x) = - 5

Apply trig inverse properties

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

Show solutions in decimal form

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

csc^{2} (θ) + 1 = cot^{2} (θ)

csc^{2} (θ) = 1

sin^{2} (θ) = cos^{2} (θ) - 1

- 5 = - 4 - 2 cos^{2} (x)

8 tan^{2} (θ) + 15 tan (θ) - 15 = 2 tan (θ) - 9

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