What is the value of sec(-405) ?

The value of sec(-405) is square root of 2

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sec(-405)

sec (- 40 5^{\circ})

2

Decimal Notation

1.41421 \dots

Solution steps

sec (- 40 5^{\circ})

Use the following property:

sec (- x) = sec (x)

sec (- 40 5^{\circ}) = sec (40 5^{\circ})

= sec (40 5^{\circ})

sec (40 5^{\circ}) = sec (4 5^{\circ})

sec (40 5^{\circ})

Rewrite

40 5^{\circ}

36 0^{\circ} + 4 5^{\circ}

= sec (36 0^{\circ} + 4 5^{\circ})

Apply the periodicity of

sec

sec (x + 36 0^{\circ}) = sec (x)

sec (36 0^{\circ} + 4 5^{\circ}) = sec (4 5^{\circ})

= sec (4 5^{\circ})

= sec (4 5^{\circ})

Use the following trivial identity:

sec (4 5^{\circ}) = 2

sec (4 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

arcsin (\frac{6}{12})

0.5 - \frac{0.5 - cos ( 0.5 )}{1 + sin ( 0.5 )}

arctan (- \frac{7}{4})

csc (\frac{- 3 π}{2})

sin (\frac{π}{2} + \frac{π}{4})