sin(x)=(123sin(70))/(184.5)

Lösung

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

x = 0.67700 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.67700 \dots + 36 0^{\circ} n

Radianten

x = 0.67700 \dots + 2 πn, x = π - 0.67700 \dots + 2 πn

Schritte zur Lösung

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

Wende die Eigenschaften der Trigonometrie an

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

Allgemeine Lösung für

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n

x = arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n

Zeige Lösungen in Dezimalform

x = 0.67700 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.67700 \dots + 36 0^{\circ} n

cot^{2} (θ) = cot (θ), 0 \leq θ \leq 2 π

cos (x) = \frac{9}{19}

cos (2 θ) = \frac{1}{4}

sec (θ) = \frac{25}{7}

sec (x) = 3, \frac{3 π}{2} \leq x \leq 2 π