What is the value of 3cos((2pi)/3) ?

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

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3cos((2pi)/3)

3 cos (\frac{2 π}{3})

- \frac{3}{2}

Decimal Notation

- 1.5

Solution steps

3 cos (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 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}

= 3 (- \frac{1}{2})

Simplify

3 (- \frac{1}{2}) : - \frac{3}{2}

3 (- \frac{1}{2})

Remove parentheses:

(- a) = - a

= - 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}

= - \frac{3}{2}

tan (37 5^{\circ})

sin (arcsin (\frac{3}{4}))

cos^{2} (15 0^{\circ}) - sin^{2} (15 0^{\circ})

tan (- 3)

1 cos (0)