What is the general solution for csc(x)=3.5 ?

The general solution for csc(x)=3.5 is x=0.28975…+2pin,x=pi-0.28975…+2pin

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csc(x)=3.5

csc (x) = 3.5

x = 0.28975 \dots + 2 πn, x = π - 0.28975 \dots + 2 πn

Solution steps

csc (x) = 3.5

Apply trig inverse properties

x = arccsc (3.5) + 2 πn, x = π - arccsc (3.5) + 2 πn

Show solutions in decimal form

x = 0.28975 \dots + 2 πn, x = π - 0.28975 \dots + 2 πn

sin (x) = 0, sin (x) = 0

cos (x) = - \frac{7}{9}, \frac{π}{2} < x < π

y, x + arctan (\frac{y}{x}) = 0

sin (45 + 2 α) = \frac{3}{2}

θ, 2 sin (θ) - 5 = 0

What is the general solution for csc(x)=3.5 ?
The general solution for csc(x)=3.5 is x=0.28975…+2pin,x=pi-0.28975…+2pin