What is the value of csc((41pi)/6) ?

The value of csc((41pi)/6) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc((41pi)/6)

csc (\frac{41 π}{6})

2

Solution steps

csc (\frac{41 π}{6})

csc (\frac{41 π}{6}) = csc (\frac{5 π}{6})

csc (\frac{41 π}{6})

Rewrite

\frac{41 π}{6}

2 π \cdot 3 + \frac{5 π}{6}

= csc (2 π 3 + \frac{5 π}{6})

Apply the periodicity of

csc

csc (x + 2 π \cdot k) = csc (x)

csc (2 π \cdot 3 + \frac{5 π}{6}) = csc (\frac{5 π}{6})

= csc (\frac{5 π}{6})

= csc (\frac{5 π}{6})

Rewrite using trig identities:

\frac{1}{sin ( \frac{5 π}{6} )}

csc (\frac{5 π}{6})

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( \frac{5 π}{6} )}

= \frac{1}{sin ( \frac{5 π}{6} )}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (\frac{5 π}{6})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{\frac{1}{2}}

Simplify

= 2

arctan (\frac{3}{248})

arcsin (sin (5))

arctan (0.333)

sin (- \frac{7 π}{8})

arccosh (\frac{13}{5})