What is the value of sec(765) ?

The value of sec(765) is square root of 2

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sec(765)

sec (76 5^{\circ})

2

Decimal Notation

1.41421 \dots

Solution steps

sec (76 5^{\circ})

sec (76 5^{\circ}) = sec (4 5^{\circ})

sec (76 5^{\circ})

Rewrite

76 5^{\circ}

36 0^{\circ} \cdot 2 + 4 5^{\circ}

= sec (36 0^{\circ} 2 + 4 5^{\circ})

Apply the periodicity of

sec

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

sec (36 0^{\circ} \cdot 2 + 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

sin^{2} (\frac{1}{2} arccos (\frac{3}{5}))

sec (\frac{- 11 π}{6})

7 sin (\frac{5 π}{4}) + 7 cos (\frac{5 π}{4})

sin (25 5^{\circ}) + sin (19 5^{\circ})

arccos (0.125)