What is the value of sec(-225) ?

The value of sec(-225) is -sqrt(2)

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sec(-225)

sec (- 22 5^{\circ})

- 2

Solution steps

sec (- 22 5^{\circ})

Use the following property:

sec (- x) = sec (x)

sec (- 22 5^{\circ}) = sec (22 5^{\circ})

= sec (22 5^{\circ})

Rewrite using trig identities:

\frac{1}{cos ( 22 5 ^{\circ} )}

= \frac{1}{cos ( 22 5 ^{\circ} )}

Rewrite using trig identities:

cos (22 5^{\circ}) = - \frac{2}{2}

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

Simplify

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

= - 2

arcsin (0.77)

arcsin (0.58)

sec (6)

- 6 sin (\frac{3 π}{4})

sec^{2} (\frac{π}{3}) \cdot (- 0.1)