cot(θ)<sqrt(3)

Lösung

cot (θ) < 3

\frac{π}{6} + πn < θ < π + πn

Intervall-Notation

(\frac{π}{6} + πn, π + πn)

Dezimale

0.52359 \dots + πn < θ < 3.14159 \dots + πn

Schritte zur Lösung

cot (θ) < 3

Wenn

cot (x) < a

dann

arccot (a) + πn < x < π + πn

arccot (3) + πn < θ < π + 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}

\frac{π}{6} + πn < θ < π + πn

cos (2 x) \leq sin (x)

sin (x) cos (2 x) \geq 0

cos (x) - \frac{1}{2} cos (2 x) > 0

sec (x) \leq 2

\frac{1}{cos ( x )} \leq 2, - π \leq x \leq π