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cos(W)=(170^2+173^2-125^2)/(2(170)(173))

Lösung

cos (W) = \frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 ( 170 ) ( 173 )}

W = 0.74584 \dots + 2 πn, W = 2 π - 0.74584 \dots + 2 πn

Radianten

W = 0.74584 \dots + 6.28318 \dots n, W = 5.53733 \dots + 6.28318 \dots n

Schritte zur Lösung

cos (W) = \frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 ( 170 ) ( 173 )}

Vereinfache

\frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 \cdot 170 \cdot 173} : \frac{10801}{14705}

\frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 \cdot 170 \cdot 173}

17 0^{2} + 17 3^{2} - 12 5^{2} = 43204

17 0^{2} + 17 3^{2} - 12 5^{2}

17 0^{2} = 28900

= 28900 + 17 3^{2} - 12 5^{2}

17 3^{2} = 29929

= 28900 + 29929 - 12 5^{2}

12 5^{2} = 15625

= 28900 + 29929 - 15625

Addiere/Subtrahiere die Zahlen:

28900 + 29929 - 15625 = 43204

= 43204

= \frac{43204}{2 \cdot 170 \cdot 173}

Multipliziere die Zahlen:

2 \cdot 170 \cdot 173 = 58820

= \frac{43204}{58820}

Streiche die gemeinsamen Faktoren:

4

= \frac{10801}{14705}

Wende die Eigenschaften der Trigonometrie an

cos (W) = \frac{10801}{14705}

Allgemeine Lösung für

cos (W) = \frac{10801}{14705}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

W = arccos (\frac{10801}{14705}) + 2 πn, W = 2 π - arccos (\frac{10801}{14705}) + 2 πn

W = arccos (\frac{10801}{14705}) + 2 πn, W = 2 π - arccos (\frac{10801}{14705}) + 2 πn

Zeige Lösungen in Dezimalform

W = 0.74584 \dots + 2 πn, W = 2 π - 0.74584 \dots + 2 πn

2 csc^{2} (x) + csc (x) - 1 = 0

tan (x) = 0.15

sec (x + 4 5^{\circ}) = 1

117.72 sin (θ) - 35.316 cos (θ) - 12.5 = 0

\frac{1}{cot ^{2} ( x )} + 3 tan (x) = 0