What is the value of sec((-7pi)/6) ?

The value of sec((-7pi)/6) is -(2sqrt(3))/3

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sec((-7pi)/6)

sec (\frac{- 7 π}{6})

- \frac{2 3}{3}

Solution steps

sec (\frac{- 7 π}{6})

Simplify

= sec (- \frac{7 π}{6})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{7 π}{6}) = sec (\frac{7 π}{6})

= sec (\frac{7 π}{6})

Rewrite using trig identities:

\frac{1}{cos ( \frac{7 π}{6} )}

= \frac{1}{cos ( \frac{7 π}{6} )}

Rewrite using trig identities:

cos (\frac{7 π}{6}) = - \frac{3}{2}

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

Simplify

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

= - \frac{2 3}{3}

ln (2 + sin (\frac{11 π}{6}))

cos (4 5^{\circ} + 15 0^{\circ})

cos (4 5^{\circ}) + sin (4 5^{\circ})

4 cos (25 0^{\circ})

\frac{cos ( - 0.001 ) - 1}{- 0.001}

What is the value of sec((-7pi)/6) ?
The value of sec((-7pi)/6) is -(2sqrt(3))/3