cot(x)>sqrt(3)

Lösung

cot (x) > 3

πn < x < \frac{π}{6} + πn

Intervall-Notation

(πn, \frac{π}{6} + πn)

Dezimale

πn < x < 0.52359 \dots + πn

Schritte zur Lösung

cot (x) > 3

Wenn

cot (x) > a

dann

πn < x < arccot (a) + πn

πn < x < arccot (3) + πn

Vereinfache

arccot (3) : \frac{π}{6}

arccot (3)

Verwende die folgende triviale Identität:

arccot (3) = \frac{π}{6}

x - 3 - 1 - \frac{3}{3} 0 \frac{3}{3} 13 arccot (x) \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} arccot (x) 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ}

= \frac{π}{6}

πn < x < \frac{π}{6} + πn

cos^{2} (x) > \frac{1}{4}

cos^{2} (x) \geq 0

cos^{2} (x) > \frac{1}{2}

sec (x) < 0

so l v e f or θ, r^{2} cos^{2} (θ) + r^{2} sin^{2} (θ) \leq 1