What is the value of 2sec(pi/6) ?

The value of 2sec(pi/6) is (4sqrt(3))/3

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2sec(pi/6)

2 sec (\frac{π}{6})

\frac{4 3}{3}

Decimal Notation

2.30940 \dots

Solution steps

2 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}

= 2 \cdot \frac{2 3}{3}

Simplify

2 \cdot \frac{2 3}{3} : \frac{4 3}{3}

2 \cdot \frac{2 3}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 3 \cdot 2}{3}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 3}{3}

= \frac{4 3}{3}

8 sin (2 0^{\circ})

arctan (0.81)

arctan (0.88)

12 \cdot cos (4 5^{\circ})

sin (- \frac{12}{13})