What is the value of sec(-135) ?

The value of sec(-135) is -sqrt(2)

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sec(-135)

sec (- 13 5^{\circ})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

sec (- 13 5^{\circ})

Use the following property:

sec (- x) = sec (x)

sec (- 13 5^{\circ}) = sec (13 5^{\circ})

= sec (13 5^{\circ})

Use the following trivial identity:

sec (13 5^{\circ}) = - 2

sec (13 5^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= - 2

= - 2

cos^{3} (2 π)

5 sin (4 5^{\circ})

sin (2 \frac{π}{2})

3 sin (\frac{π}{3})

cos (40 5^{\circ})