What is the value of sec(-(8pi)/3) ?

The value of sec(-(8pi)/3) is -2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(-(8pi)/3)

sec (- \frac{8 π}{3})

- 2

Solution steps

sec (- \frac{8 π}{3})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{8 π}{3}) = sec (\frac{8 π}{3})

= sec (\frac{8 π}{3})

sec (\frac{8 π}{3}) = sec (\frac{2 π}{3})

sec (\frac{8 π}{3})

Rewrite

\frac{8 π}{3}

2 π + \frac{2 π}{3}

= sec (2 π + \frac{2 π}{3})

Apply the periodicity of

sec

sec (x + 2 π) = sec (x)

sec (2 π + \frac{2 π}{3}) = sec (\frac{2 π}{3})

= sec (\frac{2 π}{3})

= sec (\frac{2 π}{3})

Use the following trivial identity:

sec (\frac{2 π}{3}) = - 2

sec (\frac{2 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

\frac{1}{2} arctan (0)

sin (arcsin (\frac{2 π}{3}))

csc (2 1^{\circ})

sec^{2} (3)

sin (\frac{9 π}{6})