What is the value of csc(2pi) ?

The value of csc(2pi) is Undefined

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csc(2pi)

csc (2 π)

Undefined

Solution steps

csc (2 π)

csc (2 π) = csc (0)

csc (2 π)

Rewrite

2 π

2 π + 0

= csc (2 π + 0)

Apply the periodicity of

csc

csc (x + 2 π) = csc (x)

csc (2 π + 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

sin (0)

cos (\frac{π}{3}) + cot (\frac{9 π}{4})

sin (2 θ) + cos (θ) = 0

csc (- x) - sin (- x) = - cos (x) cot (x)

cot (\frac{4 π}{3})