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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-5cos(-pi/6)

- 5 cos (- \frac{π}{6})

- \frac{5 3}{2}

Decimal Notation

- 4.33012 \dots

Solution steps

- 5 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 \cdot \frac{3}{2}

Simplify

- 5 \cdot \frac{3}{2} : - \frac{5 3}{2}

- 5 \cdot \frac{3}{2}

Multiply fractions:

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

= - \frac{3 \cdot 5}{2}

= - \frac{5 3}{2}

arctan (\frac{1}{11}) + arctan (11)

arctan (\frac{4}{3})

arcsin (1.41) sin (30. 1^{\circ})

arcsin (\frac{2}{10})

x \to \infty lim (arctan (\frac{x}{2}))