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人気のある三角関数 >

-sin(A)+2cos(A)sin(A)=0

解

- sin (A) + 2 cos (A) sin (A) = 0

解

A = 2 πn, A = π + 2 πn, A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn

+1

度

A = 0^{\circ} + 36 0^{\circ} n, A = 18 0^{\circ} + 36 0^{\circ} n, A = 6 0^{\circ} + 36 0^{\circ} n, A = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

- sin (A) + 2 cos (A) sin (A) = 0

因数

- sin (A) + 2 cos (A) sin (A) : sin (A) (2 cos (A) - 1)

- sin (A) + 2 cos (A) sin (A)

共通項をくくり出す

sin (A)

= sin (A) (- 1 + 2 cos (A))

sin (A) (2 cos (A) - 1) = 0

各部分を別個に解く

sin (A) = 0 or 2 cos (A) - 1 = 0

sin (A) = 0 : A = 2 πn, A = π + 2 πn

sin (A) = 0

以下の一般解

sin (A) = 0

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

A = 0 + 2 πn, A = π + 2 πn

A = 0 + 2 πn, A = π + 2 πn

解く

A = 0 + 2 πn : A = 2 πn

A = 0 + 2 πn

0 + 2 πn = 2 πn

A = 2 πn

A = 2 πn, A = π + 2 πn

2 cos (A) - 1 = 0 : A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn

2 cos (A) - 1 = 0

1

を右側に移動します

2 cos (A) - 1 = 0

両辺に

1

を足す

2 cos (A) - 1 + 1 = 0 + 1

簡素化

2 cos (A) = 1

2 cos (A) = 1

以下で両辺を割る

2

2 cos (A) = 1

以下で両辺を割る

2

\frac{2 cos ( A )}{2} = \frac{1}{2}

簡素化

cos (A) = \frac{1}{2}

cos (A) = \frac{1}{2}

以下の一般解

cos (A) = \frac{1}{2}

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}

A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn

A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn

すべての解を組み合わせる

A = 2 πn, A = π + 2 πn, A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn

グラフ

人気の例

3tan(θ)=-3,0<= θ<= 2pi

3 tan (θ) = - 3, 0 \leq θ \leq 2 π

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2 cot^{2} (x) - csc^{2} (x) + csc (x) = 4

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\frac{cot ( x )}{sec ( x )} = sin (x)

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sec^{2} (θ) tan (θ) = 2 tan (θ), 0 \leq θ \leq 2 π