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

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

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-sec((-pi)/3)

- sec (\frac{- π}{3})

- 2

Solution steps

- sec (\frac{- π}{3})

Rewrite using trig identities:

sec (\frac{- π}{3}) = 2

sec (\frac{- π}{3})

Simplify

= sec (- \frac{π}{3})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{π}{3}) = sec (\frac{π}{3})

= sec (\frac{π}{3})

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{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

= - 2

csc (4 6^{\circ})

8 sin (18 0^{\circ})

- cos (- \frac{5 π}{3})

sin (\frac{2 π}{12})

arctan (\frac{700 - 1000}{400})