What is the general solution for csc(x)= 21/5 ?

The general solution for csc(x)= 21/5 is x=0.24040…+2pin,x=pi-0.24040…+2pin

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csc(x)= 21/5

csc (x) = \frac{21}{5}

x = 0.24040 \dots + 2 πn, x = π - 0.24040 \dots + 2 πn

Solution steps

csc (x) = \frac{21}{5}

Apply trig inverse properties

x = arccsc (\frac{21}{5}) + 2 πn, x = π - arccsc (\frac{21}{5}) + 2 πn

Show solutions in decimal form

x = 0.24040 \dots + 2 πn, x = π - 0.24040 \dots + 2 πn

3 cot (2 x) + 3 = 0

\frac{1}{cos ( θ )} = 2

θ, r = sin (2 θ)

cos (θ) = \frac{7}{25}, \frac{3 π}{2} < θ < 2 π

5 (1 - sin (θ)) = 5

What is the general solution for csc(x)= 21/5 ?
The general solution for csc(x)= 21/5 is x=0.24040…+2pin,x=pi-0.24040…+2pin