What is the value of cos(1/3 pi)*15 ?

The value of cos(1/3 pi)*15 is 15/2

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cos(1/3 pi)*15

cos (\frac{1}{3} π) \cdot 15

\frac{15}{2}

Decimal

7.5

Solution steps

cos (\frac{1}{3} π) \cdot 15

Rewrite using trig identities:

cos (\frac{1}{3} π) = \frac{1}{2}

cos (\frac{1}{3} π)

Simplify:

\frac{1}{3} π = \frac{π}{3}

\frac{1}{3} π

Multiply fractions:

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

= \frac{1 π}{3}

Multiply:

1 π = π

= \frac{π}{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}

= \frac{1}{2}

= \frac{1}{2} \cdot 15

Simplify

\frac{1}{2} \cdot 15 : \frac{15}{2}

\frac{1}{2} \cdot 15

Convert element to fraction:

15 = \frac{15}{1}

= \frac{1}{2} \cdot \frac{15}{1}

Multiply fractions:

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

= \frac{1 \cdot 15}{2 \cdot 1}

Cancel the common factor:

1

= \frac{15}{2}

= \frac{15}{2}