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

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2sec(-pi/3)

2 sec (- \frac{π}{3})

4

Solution steps

2 sec (- \frac{π}{3})

Rewrite using trig identities:

sec (- \frac{π}{3}) = 2

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 \cdot 2

Simplify

= 4

cos (\frac{π}{6}) cos (\frac{π}{3}) - sin (\frac{π}{6}) sin (\frac{π}{3})

100 sin (9 0^{\circ})

cos^{2} (\frac{π}{6}) - 2 sin (\frac{π}{6})

arctan (\frac{7.7}{14})

arctan (tan (2))