What is the value of pi/6+2cos(pi/6) ?

The value of pi/6+2cos(pi/6) is pi/6+sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

pi/6+2cos(pi/6)

\frac{π}{6} + 2 cos (\frac{π}{6})

\frac{π}{6} + 3

Decimal Notation

2.25564 \dots

Solution steps

\frac{π}{6} + 2 cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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

= \frac{3}{2}

= \frac{π}{6} + 2 \cdot \frac{3}{2}

Simplify

\frac{π}{6} + 2 \cdot \frac{3}{2} : \frac{π}{6} + 3

\frac{π}{6} + 2 \cdot \frac{3}{2}

2 \cdot \frac{3}{2} = 3

2 \cdot \frac{3}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 2}{2}

Cancel the common factor:

2

= 3

= \frac{π}{6} + 3

= \frac{π}{6} + 3

arctan (0.13)

6 sin (- \frac{π}{2})

\frac{sin ( 4 5 ^{\circ} ) sin ( 1 5 ^{\circ} )}{cos ( 13 5 ^{\circ} ) cos ( 10 5 ^{\circ} )}

\frac{sec ^{2} ( 0 ) - tan ^{2} ( 0 )}{1 + cot ^{2} ( 0 )}

cos (20 5^{\circ})

What is the value of pi/6+2cos(pi/6) ?
The value of pi/6+2cos(pi/6) is pi/6+sqrt(3)