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人気のある三角関数 >

3sin(x+20)-0.75=0

解

3 sin (x + 2 0^{\circ}) - 0.75 = 0

解

x = 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}

+1

ラジアン

x = 0.25268 \dots - \frac{π}{9} + 2 πn, x = π - 0.25268 \dots - \frac{π}{9} + 2 πn

解答ステップ

3 sin (x + 2 0^{\circ}) - 0.75 = 0

0.75

を右側に移動します

3 sin (x + 2 0^{\circ}) - 0.75 = 0

両辺に

0.75

を足す

3 sin (x + 2 0^{\circ}) - 0.75 + 0.75 = 0 + 0.75

簡素化

3 sin (x + 2 0^{\circ}) = 0.75

3 sin (x + 2 0^{\circ}) = 0.75

以下で両辺を割る

3

3 sin (x + 2 0^{\circ}) = 0.75

以下で両辺を割る

3

\frac{3 sin ( x + 2 0 ^{\circ} )}{3} = \frac{0.75}{3}

簡素化

sin (x + 2 0^{\circ}) = 0.25

sin (x + 2 0^{\circ}) = 0.25

三角関数の逆数プロパティを適用する

sin (x + 2 0^{\circ}) = 0.25

以下の一般解

sin (x + 2 0^{\circ}) = 0.25

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

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

解く

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n : x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n

2 0^{\circ}

を右側に移動します

x + 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n

両辺から

2 0^{\circ}

を引く

x + 2 0^{\circ} - 2 0^{\circ} = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

簡素化

x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

解く

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

2 0^{\circ}

を右側に移動します

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n

両辺から

2 0^{\circ}

を引く

x + 2 0^{\circ} - 2 0^{\circ} = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

簡素化

x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - arcsin (0.25) + 36 0^{\circ} n - 2 0^{\circ}

10進法形式で解を証明する

x = 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 0.25268 \dots + 36 0^{\circ} n - 2 0^{\circ}

グラフ

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