What is the value of csc(6pi) ?

The value of csc(6pi) is Undefined

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csc(6pi)

csc (6 π)

Undefined

Solution steps

csc (6 π)

csc (6 π) = csc (0)

csc (6 π)

Rewrite

6 π

2 π \cdot 3 + 0

= csc (2 π 3 + 0)

Apply the periodicity of

csc

csc (x + 2 π \cdot k) = csc (x)

csc (2 π \cdot 3 + 0) = csc (0)

= csc (0)

= csc (0)

Rewrite using trig identities:

Undefined

csc (0)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( 0 )}

Simplify

\frac{1}{sin ( 0 )} :

Undefined

\frac{1}{sin ( 0 )}

sin (0) = 0

= \frac{1}{0}

\frac{x}{0}

is undefined

= Undefined

= Undefined

= Undefined

tan (\frac{25 π}{4})

e^{- 1} sin (1)

cos^{2} (4 5^{\circ}) + sin^{2} (4 5^{\circ})

\frac{2 tan ( 4 2 ^{\circ} )}{1 - tan ( 4 2 ^{\circ} )}

e^{- \frac{π}{2}} sin (\frac{π}{2})