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

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

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cos(pi-pi/3)

cos (π - \frac{π}{3})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

cos (π - \frac{π}{3})

Simplify:

π - \frac{π}{3} = \frac{2 π}{3}

π - \frac{π}{3}

Convert element to fraction:

π = \frac{π 3}{3}

= \frac{π 3}{3} - \frac{π}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{π 3 - π}{3}

Add similar elements:

3 π - π = 2 π

= \frac{2 π}{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}

= - \frac{1}{2}

\frac{12.2}{sin ( 4 0 ^{\circ} )}

cos (3 0^{\circ}) sin (4 5^{\circ}) + sin (3 0^{\circ}) tan (3 0^{\circ})

sin (252 0^{\circ})

tan (arcsin (\frac{- 4}{5}))

cos (5 π \frac{1}{6})