Februar 6, 2020

von Gael

Wie bewerten Sie $cos (\frac{2 π}{3})$ $cos ((2pi) / 3)$ ?

Antworten:

$- \frac{1}{2}$ $-1/2$

Erläuterung:

The angle $\frac{2 π}{3} is in the 2nd quadrant$ $(2pi)/3" is in the 2nd quadrant "$
where the cos ratio has a negative value.

The related 'acute angle' to $\frac{2 π}{3} = (π - \frac{2 π}{3}) = \frac{π}{3}$ $(2pi)/3 =( pi -(2pi)/3) = pi/3$

$\Rightarrow cos (\frac{2 π}{3}) = - cos (\frac{π}{3})$ $rArr cos((2pi)/3) = - cos(pi/3)$

and using the $Exact value triangle$ $color(blue)" Exact value triangle"$

Bildquelle hier eingeben

$cos (\frac{2 π}{3}) = - cos (\frac{π}{3}) = - \frac{1}{2}$ $cos((2pi)/3) = - cos(pi/3) = -1/2$