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العربية

0.175=0.34sin(93.4t)

Lösung

0.175 = 0.34 sin (93.4 t)

t = \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}, t = \frac{π}{93.4} - \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}

Grad

t = 0.33166 \dots^{\circ} + 3.85438 \dots^{\circ} n, t = 1.59552 \dots^{\circ} + 3.85438 \dots^{\circ} n

Schritte zur Lösung

0.175 = 0.34 sin (93.4 t)

Tausche die Seiten

0.34 sin (93.4 t) = 0.175

Multipliziere beide Seiten mit

1000

0.34 sin (93.4 t) = 0.175

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

0.34 sin (93.4 t) \cdot 1000 = 0.175 \cdot 1000

Fasse zusammen

340 sin (93.4 t) = 175

340 sin (93.4 t) = 175

Teile beide Seiten durch

340

340 sin (93.4 t) = 175

Teile beide Seiten durch

340

\frac{340 sin ( 93.4 t )}{340} = \frac{175}{340}

Vereinfache

sin (93.4 t) = \frac{35}{68}

sin (93.4 t) = \frac{35}{68}

Wende die Eigenschaften der Trigonometrie an

sin (93.4 t) = \frac{35}{68}

Allgemeine Lösung für

sin (93.4 t) = \frac{35}{68}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

93.4 t = arcsin (\frac{35}{68}) + 2 πn, 93.4 t = π - arcsin (\frac{35}{68}) + 2 πn

93.4 t = arcsin (\frac{35}{68}) + 2 πn, 93.4 t = π - arcsin (\frac{35}{68}) + 2 πn

Löse

93.4 t = arcsin (\frac{35}{68}) + 2 πn : t = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

93.4 t = arcsin (\frac{35}{68}) + 2 πn

Teile beide Seiten durch

93.4

93.4 t = arcsin (\frac{35}{68}) + 2 πn

Teile beide Seiten durch

93.4

\frac{93.4 t}{93.4} = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Vereinfache

t = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

t = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Löse

93.4 t = π - arcsin (\frac{35}{68}) + 2 πn : t = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

93.4 t = π - arcsin (\frac{35}{68}) + 2 πn

Teile beide Seiten durch

93.4

93.4 t = π - arcsin (\frac{35}{68}) + 2 πn

Teile beide Seiten durch

93.4

\frac{93.4 t}{93.4} = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Vereinfache

t = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

t = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

t = \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}, t = \frac{π}{93.4} - \frac{arcsin ( \frac{35}{68} )}{93.4} + \frac{2 πn}{93.4}

Zeige Lösungen in Dezimalform

t = \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}, t = \frac{π}{93.4} - \frac{0.54066 \dots}{93.4} + \frac{2 πn}{93.4}

4 cos^{2} (x) - 6 = 5 cos (x)

tan (θ) = \frac{- 3}{2}

2 sin (x) tan (2 x) - 3 tan (2 x) = 0

tan (x) = \frac{12}{8}

cos (2 t) - cos (t) = - 0.5, 0 \leq t \leq 2 π