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人気のある三角関数 >

5sin(x)cos(x)=2cos(x)

解

5 sin (x) cos (x) = 2 cos (x)

解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

+1

度

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 23.57817 \dots^{\circ} + 36 0^{\circ} n, x = 156.42182 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

5 sin (x) cos (x) = 2 cos (x)

両辺から

2 cos (x)

を引く

5 sin (x) cos (x) - 2 cos (x) = 0

因数

5 sin (x) cos (x) - 2 cos (x) : cos (x) (5 sin (x) - 2)

5 sin (x) cos (x) - 2 cos (x)

共通項をくくり出す

cos (x)

= cos (x) (5 sin (x) - 2)

cos (x) (5 sin (x) - 2) = 0

各部分を別個に解く

cos (x) = 0 or 5 sin (x) - 2 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

以下の一般解

cos (x) = 0

cos (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

5 sin (x) - 2 = 0 : x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

5 sin (x) - 2 = 0

2

を右側に移動します

5 sin (x) - 2 = 0

両辺に

2

を足す

5 sin (x) - 2 + 2 = 0 + 2

簡素化

5 sin (x) = 2

5 sin (x) = 2

以下で両辺を割る

5

5 sin (x) = 2

以下で両辺を割る

5

\frac{5 sin ( x )}{5} = \frac{2}{5}

簡素化

sin (x) = \frac{2}{5}

sin (x) = \frac{2}{5}

三角関数の逆数プロパティを適用する

sin (x) = \frac{2}{5}

以下の一般解

sin (x) = \frac{2}{5}

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

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

すべての解を組み合わせる

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

10進法形式で解を証明する

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

グラフ

人気の例

sin(x)=cos^3(x)

sin (x) = cos^{3} (x)

a=((1+sin^2(x)))/((1-sin^2(x)))

a = \frac{( 1 + sin ^{2} ( x ) )}{( 1 - sin ^{2} ( x ) )}

solvefor x,b*f=sin^3(x)

so l v e f or x, b \cdot f = sin^{3} (x)

2sin^2(x)+sin^3(x)-1=0

2 sin^{2} (x) + sin^{3} (x) - 1 = 0

2cos^2(x)=3cos(x)-1

2 cos^{2} (x) = 3 cos (x) - 1