What is the value of sec(((2pi))/3) ?

The value of sec(((2pi))/3) is -2

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Find the Exact Value sec((2pi)/3)

sec (\frac{( 2 π )}{3})

- 2

Solution steps

sec (\frac{( 2 π )}{3})

= sec (\frac{2 π}{3})

Use the following trivial identity:

sec (\frac{2 π}{3}) = - 2

sec (\frac{2 π}{3})

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}

= - 2

= - 2

sin (\frac{135}{2})

cos (\frac{( 5 π )}{6})

cos (θ) = \frac{4}{5}, 27 0^{\circ} < θ < 36 0^{\circ}

tan (\frac{( 5 π )}{6})

sin (\frac{200}{90})