What is the value of sec((11pi)/2) ?

The value of sec((11pi)/2) is Undefined

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sec((11pi)/2)

sec (\frac{11 π}{2})

Undefined

Solution steps

sec (\frac{11 π}{2})

sec (\frac{11 π}{2}) = sec (\frac{3 π}{2})

sec (\frac{11 π}{2})

Rewrite

\frac{11 π}{2}

2 π \cdot 2 + \frac{3 π}{2}

= sec (2 π 2 + \frac{3 π}{2})

Apply the periodicity of

sec

sec (x + 2 π \cdot k) = sec (x)

sec (2 π \cdot 2 + \frac{3 π}{2}) = sec (\frac{3 π}{2})

= sec (\frac{3 π}{2})

= sec (\frac{3 π}{2})

Rewrite using trig identities:

Undefined

sec (\frac{3 π}{2})

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( \frac{3 π}{2} )}

Simplify

\frac{1}{cos ( \frac{3 π}{2} )} :

Undefined

\frac{1}{cos ( \frac{3 π}{2} )}

cos (\frac{3 π}{2}) = 0

= \frac{1}{0}

\frac{x}{0}

is undefined

= Undefined

= Undefined

= Undefined

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