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

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sec(-3pi)

sec (- 3 π)

- 1

Solution steps

sec (- 3 π)

Use the following property:

sec (- x) = sec (x)

sec (- 3 π) = sec (3 π)

= sec (3 π)

sec (3 π) = sec (π)

sec (3 π)

Rewrite

3 π

2 π + π

= sec (2 π + π)

Apply the periodicity of

sec

sec (x + 2 π) = sec (x)

sec (2 π + π) = sec (π)

= sec (π)

= sec (π)

Use the following trivial identity:

sec (π) = (- 1)

sec (π)

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}

= (- 1)

= - 1

sin^{3} (\frac{π}{3})

tan (45 0^{\circ})

tan (- 30 0^{\circ})

arctan (\frac{40}{30})

cos (arcsin (- \frac{3}{5}))