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

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

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sec(-pi/3)tan(-pi/3)

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

- 23

Decimal Notation

- 3.46410 \dots

Solution steps

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

Use the following property:

tan (- x) = - tan (x)

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

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

Use the following property:

sec (- x) = sec (x)

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

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

Simplify

= - sec (\frac{π}{3}) tan (\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

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

= - 23

sec (1 6^{\circ})

2 π - 2 sin (2 π)

sin (5) - sin (1)

cos (3) (\frac{π}{6})

arctan (- \frac{1}{- 1})

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