What is the value of sec((-11pi)/3) ?

The value of sec((-11pi)/3) is 2

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sec((-11pi)/3)

sec (\frac{- 11 π}{3})

2

Solution steps

sec (\frac{- 11 π}{3})

Simplify

= sec (- \frac{11 π}{3})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{11 π}{3}) = sec (\frac{11 π}{3})

= sec (\frac{11 π}{3})

sec (\frac{11 π}{3}) = sec (\frac{5 π}{3})

= sec (\frac{5 π}{3})

Rewrite using trig identities:

\frac{1}{cos ( \frac{5 π}{3} )}

= \frac{1}{cos ( \frac{5 π}{3} )}

Rewrite using trig identities:

cos (\frac{5 π}{3}) = \frac{1}{2}

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

Simplify

= 2

sin (- \frac{4}{7})

\frac{1}{2 ( sin ( 1 ) + cos ( 1 ) )}

tan (3 5^{\circ}) \cdot 15.6

\frac{200}{tan ( 4 0 ^{\circ} )}

22 cos (3 8^{\circ})