What is the general solution for csc(x)= 9/(sqrt(17)) ?

The general solution for csc(x)= 9/(sqrt(17)) is x=0.47588…+2pin,x=pi-0.47588…+2pin

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csc(x)= 9/(sqrt(17))

csc (x) = \frac{9}{17}

x = 0.47588 \dots + 2 πn, x = π - 0.47588 \dots + 2 πn

Radians

x = 0.47588 \dots + 6.28318 \dots n, x = π - 0.47588 \dots + 6.28318 \dots n

Solution steps

csc (x) = \frac{9}{17}

Simplify

\frac{9}{17} : \frac{9 17}{17}

\frac{9}{17}

Multiply by the conjugate

\frac{17}{17}

= \frac{9 17}{17 17}

1717 = 17

1717

Apply radical rule:

a a = a

1717 = 17

= 17

= \frac{9 17}{17}

csc (x) = \frac{9 17}{17}

Apply trig inverse properties

csc (x) = \frac{9 17}{17}

General solutions for

csc (x) = \frac{9 17}{17}

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

x = arccsc (\frac{9 17}{17}) + 2 πn, x = π - arccsc (\frac{9 17}{17}) + 2 πn

x = arccsc (\frac{9 17}{17}) + 2 πn, x = π - arccsc (\frac{9 17}{17}) + 2 πn

Show solutions in decimal form

x = 0.47588 \dots + 2 πn, x = π - 0.47588 \dots + 2 πn

What is the general solution for csc(x)= 9/(sqrt(17)) ?
The general solution for csc(x)= 9/(sqrt(17)) is x=0.47588…+2pin,x=pi-0.47588…+2pin