What is the value of sec(pi/6)-sec(0) ?

The value of sec(pi/6)-sec(0) is (2sqrt(3))/3-1

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sec(pi/6)-sec(0)

sec (\frac{π}{6}) - sec (0)

\frac{2 3}{3} - 1

Decimal Notation

0.15470 \dots

Solution steps

sec (\frac{π}{6}) - sec (0)

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}

Use the following trivial identity:

sec (0) = 1

sec (0)

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}

= 1

= \frac{2 3}{3} - 1

1.5 sin (4 5^{\circ})

20 [cos (\frac{7 π}{6}) + i sin (\frac{7 π}{6})]

arccos (- 0.447)

cos (2) e^{0}

1 - 2 sin^{2} (1 9^{\circ})

What is the value of sec(pi/6)-sec(0) ?
The value of sec(pi/6)-sec(0) is (2sqrt(3))/3-1