cot(θ)<0,sec(θ)>0

Lösung

cot (θ) < 0, sec (θ) > 0

\frac{π}{2} + πn < θ < π + πn

Intervall-Notation

(\frac{π}{2} + πn, π + πn)

Dezimale

1.57079 \dots + πn < θ < 3.14159 \dots + πn

Schritte zur Lösung

cot (θ) < 0

Wenn

cot (x) < a

dann

arccot (a) + πn < x < π + πn

arccot (0) + πn < θ < π + πn

Vereinfache

arccot (0) : \frac{π}{2}

arccot (0)

Verwende die folgende triviale Identität:

arccot (0) = \frac{π}{2}

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}{2}

\frac{π}{2} + πn < θ < π + πn

cos (θ) > 0, cot (θ) > 0

sec (x) < - 1

1 + cos (x) \geq 0

(sin (x) + cos (x))^{2} \geq 3 - 2 tan (x) + tan^{2} (x)

3 cos (x) - sin (x) \leq 0