What is the value of sec(-(13pi)/4) ?

The value of sec(-(13pi)/4) is -sqrt(2)

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sec(-(13pi)/4)

sec (- \frac{13 π}{4})

- 2

Solution steps

sec (- \frac{13 π}{4})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{13 π}{4}) = sec (\frac{13 π}{4})

= sec (\frac{13 π}{4})

sec (\frac{13 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

arccos (\frac{4}{4 2})

- 2 sec (9 0^{\circ})

arctan (1.44)

6 sin (3 5^{\circ})

3.7 \cdot sin (3 0^{\circ})