arccos(x)= pi/3

Lösung

arccos (x) = \frac{π}{3}

x = \frac{1}{2}

Schritte zur Lösung

arccos (x) = \frac{π}{3}

Wende die Eigenschaften der Trigonometrie an

arccos (x) = \frac{π}{3}

arccos (x) = a \Rightarrow x = cos (a)

x = cos (\frac{π}{3})

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

Verwende die folgende triviale Identität:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (x)

Periodizitätstabelle mit

2 πn

Zyklus:

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}

x = \frac{1}{2}

x = \frac{1}{2}

arccos (x) = \frac{π}{2}

tan (10 x) = cot (5 x)

sin (x) = \frac{4.5}{11.75}

sin (x) - 6 cos (x) = 0

4 sin (3 x) = 0