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人気のある三角関数 >

6.15=220sin(377t)

解

6.15 = 220 sin (377 t)

解

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

+1

度

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

解答ステップ

6.15 = 220 sin (377 t)

辺を交換する

220 sin (377 t) = 6.15

以下で両辺を割る

220

220 sin (377 t) = 6.15

以下で両辺を割る

220

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

簡素化

sin (377 t) = 0.02795 \dots

sin (377 t) = 0.02795 \dots

三角関数の逆数プロパティを適用する

sin (377 t) = 0.02795 \dots

以下の一般解

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

解く

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

以下で両辺を割る

377

377 t = arcsin (0.02795 \dots) + 2 πn

以下で両辺を割る

377

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

簡素化

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

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

解く

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

以下で両辺を割る

377

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

以下で両辺を割る

377

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

簡素化

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}

10進法形式で解を証明する

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

グラフ

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