What is the value of sec((-5pi)/4) ?

The value of sec((-5pi)/4) is -sqrt(2)

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sec((-5pi)/4)

sec (\frac{- 5 π}{4})

- 2

Solution steps

sec (\frac{- 5 π}{4})

Simplify

= sec (- \frac{5 π}{4})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{5 π}{4}) = sec (\frac{5 π}{4})

= sec (\frac{5 π}{4})

Rewrite using trig identities:

\frac{1}{cos ( \frac{5 π}{4} )}

= \frac{1}{cos ( \frac{5 π}{4} )}

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

= \frac{1}{- \frac{2}{2}}

Simplify

\frac{1}{- \frac{2}{2}} : - 2

= - 2

cos (68. 2^{\circ})

cos (- 4 0^{\circ})

tan (2 arcsin (\frac{5}{13}))

- cos (2 π) + cos (0)

arccos (\frac{2}{2 2})