What is the value of 5+4cos(-pi/6) ?

The value of 5+4cos(-pi/6) is 5+2sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

5+4cos(-pi/6)

5 + 4 cos (- \frac{π}{6})

5 + 23

Decimal

8.46410 \dots

Solution steps

5 + 4 cos (- \frac{π}{6})

Rewrite using trig identities:

cos (- \frac{π}{6}) = \frac{3}{2}

cos (- \frac{π}{6})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{6}) = cos (\frac{π}{6})

= 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{3}{2}

= 5 + 4 \cdot \frac{3}{2}

Simplify

5 + 4 \cdot \frac{3}{2} : 5 + 23

5 + 4 \cdot \frac{3}{2}

4 \cdot \frac{3}{2} = 23

4 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 23

= 5 + 23

= 5 + 23