What is the value of 4+3cos(pi/3) ?

The value of 4+3cos(pi/3) is 11/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4+3cos(pi/3)

4 + 3 cos (\frac{π}{3})

\frac{11}{2}

Decimal Notation

5.5

Solution steps

4 + 3 cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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{1}{2}

= 4 + 3 \cdot \frac{1}{2}

Simplify

4 + 3 \cdot \frac{1}{2} : \frac{11}{2}

4 + 3 \cdot \frac{1}{2}

3 \cdot \frac{1}{2} = \frac{3}{2}

3 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 3}{2}

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{2}

= 4 + \frac{3}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

4 \cdot 2 + 3 = 11

4 \cdot 2 + 3

Multiply the numbers:

4 \cdot 2 = 8

= 8 + 3

Add the numbers:

8 + 3 = 11

= 11

= \frac{11}{2}

= \frac{11}{2}

arctan (- 0.09)

arccos (\frac{1}{2}) + 2 arcsin (\frac{1}{2})

\frac{tan ( 30 0 ^{\circ} )}{sin ( 12 0 ^{\circ} )}

cos (\frac{8 π}{7})

15 cos (5 0^{\circ})