What is the value of (sec(32pi))/3 ?

The value of (sec(32pi))/3 is 1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(sec(32pi))/3

\frac{sec ( 32 π )}{3}

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

\frac{sec ( 32 π )}{3}

sec (32 π) = sec (0)

sec (32 π)

Rewrite

32 π

2 π \cdot 16 + 0

= sec (2 π 16 + 0)

Apply the periodicity of

sec

sec (x + 2 π \cdot k) = sec (x)

sec (2 π \cdot 16 + 0) = sec (0)

= sec (0)

= \frac{sec ( 0 )}{3}

Use the following trivial identity:

sec (0) = 1

sec (0)

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

= \frac{1}{3}