What is the value of sec((-4pi)/3) ?

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

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sec((-4pi)/3)

sec (\frac{- 4 π}{3})

- 2

Solution steps

sec (\frac{- 4 π}{3})

Simplify

= sec (- \frac{4 π}{3})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{4 π}{3}) = sec (\frac{4 π}{3})

= sec (\frac{4 π}{3})

Rewrite using trig identities:

\frac{1}{cos ( \frac{4 π}{3} )}

= \frac{1}{cos ( \frac{4 π}{3} )}

Rewrite using trig identities:

cos (\frac{4 π}{3}) = - \frac{1}{2}

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

Simplify

= - 2

2 sin (1 5^{\circ})

sin (- 0.3)

\frac{cos ( 5 π )}{6}

arctan (cos (\frac{π}{2}))

sin (arctan (3))