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6.15=220sin(377t)

Soluzione

6.15 = 220 sin (377 t)

t = \frac{0.02795 \dots}{377} + \frac{2 πn}{377}, t = \frac{π}{377} - \frac{0.02795 \dots}{377} + \frac{2 πn}{377}

Gradi

t = 0.00424 \dots^{\circ} + 0.95490 \dots^{\circ} n, t = 0.47320 \dots^{\circ} + 0.95490 \dots^{\circ} n

Fasi della soluzione

6.15 = 220 sin (377 t)

Scambia i lati

220 sin (377 t) = 6.15

Dividere entrambi i lati per

220

220 sin (377 t) = 6.15

Dividere entrambi i lati per

220

\frac{220 sin ( 377 t )}{220} = \frac{6.15}{220}

Semplificare

sin (377 t) = 0.02795 \dots

sin (377 t) = 0.02795 \dots

Applica le proprietà inverse delle funzioni trigonometriche

sin (377 t) = 0.02795 \dots

Soluzioni generali per

sin (377 t) = 0.02795 \dots

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

377 t = arcsin (0.02795 \dots) + 2 πn, 377 t = π - arcsin (0.02795 \dots) + 2 πn

377 t = arcsin (0.02795 \dots) + 2 πn, 377 t = π - arcsin (0.02795 \dots) + 2 πn

Risolvi

377 t = arcsin (0.02795 \dots) + 2 πn : t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

377 t = arcsin (0.02795 \dots) + 2 πn

Dividere entrambi i lati per

377

377 t = arcsin (0.02795 \dots) + 2 πn

Dividere entrambi i lati per

377

\frac{377 t}{377} = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Semplificare

t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Risolvi

377 t = π - arcsin (0.02795 \dots) + 2 πn : t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

377 t = π - arcsin (0.02795 \dots) + 2 πn

Dividere entrambi i lati per

377

377 t = π - arcsin (0.02795 \dots) + 2 πn

Dividere entrambi i lati per

377

\frac{377 t}{377} = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Semplificare

t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

t = \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}, t = \frac{π}{377} - \frac{arcsin ( 0.02795 \dots )}{377} + \frac{2 πn}{377}

Mostra le soluzioni in forma decimale

t = \frac{0.02795 \dots}{377} + \frac{2 πn}{377}, t = \frac{π}{377} - \frac{0.02795 \dots}{377} + \frac{2 πn}{377}

so l v e f or x, 3 sec (5 x) - 2 = 0

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sin (x) = \frac{14}{16}

csc (A) = 1.2384