What is the value of sec((25pi)/6) ?

The value of sec((25pi)/6) is (2sqrt(3))/3

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sec((25pi)/6)

sec (\frac{25 π}{6})

\frac{2 3}{3}

Decimal Notation

1.15470 \dots

Solution steps

sec (\frac{25 π}{6})

sec (\frac{25 π}{6}) = sec (\frac{π}{6})

sec (\frac{25 π}{6})

Rewrite

\frac{25 π}{6}

2 π \cdot 2 + \frac{π}{6}

= sec (2 π 2 + \frac{π}{6})

Apply the periodicity of

sec

sec (x + 2 π \cdot k) = sec (x)

sec (2 π \cdot 2 + \frac{π}{6}) = sec (\frac{π}{6})

= sec (\frac{π}{6})

= sec (\frac{π}{6})

Use the following trivial identity:

sec (\frac{π}{6}) = \frac{2 3}{3}

sec (\frac{π}{6})

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

= \frac{2 3}{3}

sin (4 5^{\circ}) + sin (6 0^{\circ})

cos (28 0^{\circ})

sin (\frac{3 π}{4}) - cos (\frac{3 π}{4})

\frac{6.4}{sin ( 4 2 ^{\circ} )}

sin (- \frac{17 π}{12})