What is the value of 4sec(2pi) ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4sec(2pi)

4 sec (2 π)

4

Solution steps

4 sec (2 π)

Rewrite using trig identities:

sec (2 π) = 1

sec (2 π)

sec (2 π) = sec (0)

sec (2 π)

Rewrite

2 π

2 π + 0

= sec (2 π + 0)

Apply the periodicity of

sec

sec (x + 2 π) = sec (x)

sec (2 π + 0) = sec (0)

= sec (0)

= sec (0)

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

= 1

= 4 \cdot 1

Simplify

= 4

cos^{3} (1)

\frac{tan ( 5 ^{\circ} ) + tan ( 2 5 ^{\circ} )}{1 - tan ( 5 ^{\circ} ) tan ( 2 5 ^{\circ} )}

arctan (1.25)

arctan (\frac{7}{6})

sin (arctan (\frac{5}{12}))