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

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-4cos(pi/3)

- 4 cos (\frac{π}{3})

- 2

Solution steps

- 4 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 \cdot \frac{1}{2}

Simplify

- 4 \cdot \frac{1}{2} : - 2

- 4 \cdot \frac{1}{2}

Convert element to fraction:

4 = \frac{4}{1}

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

Cross-cancel common factor:

2

= - \frac{2}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{2}{1} = 2

= - 2

= - 2

cos (65. 7^{\circ})

120 (tan (32. 3^{\circ}))

\frac{tan ( 6 0 ^{\circ} ) - tan ( 4 5 ^{\circ} )}{1 + tan ( 6 0 ^{\circ} ) tan ( 4 5 ^{\circ} )}

cos (- 1410 \circ)

\frac{cos ( 9 0 ^{\circ} ) + cos ( 0 )}{2 cos ( 5 0 ^{\circ} )}