What is the value of -5cos((2pi)/3) ?

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

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-5cos((2pi)/3)

- 5 cos (\frac{2 π}{3})

\frac{5}{2}

Decimal Notation

2.5

Solution steps

- 5 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}

= - 5 (- \frac{1}{2})

Simplify

- 5 (- \frac{1}{2}) : \frac{5}{2}

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

Apply rule

- (- a) = a

= 5 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 5}{2}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{2}

= \frac{5}{2}

sin (19 5^{\circ}) cos (7 5^{\circ})

\frac{8.3}{cos ( 32.1 1 ^{\circ} )}

tan^{2} (4 5^{\circ} - \frac{40}{2})

arccos (- \frac{3}{13})

tan (4 0^{\circ}) \cdot 15