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人気のある三角関数 >

4sin^2(x)+2sin(x)=2,0<= x<= 2pi

解

4 sin^{2} (x) + 2 sin (x) = 2, 0 \leq x \leq 2 π

解

x = \frac{π}{6}, x = \frac{5 π}{6}, x = \frac{3 π}{2}

+1

度

x = 3 0^{\circ}, x = 15 0^{\circ}, x = 27 0^{\circ}

解答ステップ

4 sin^{2} (x) + 2 sin (x) = 2, 0 \leq x \leq 2 π

置換で解く

4 sin^{2} (x) + 2 sin (x) = 2

仮定:

sin (x) = u

4 u^{2} + 2 u = 2

4 u^{2} + 2 u = 2 : u = \frac{1}{2}, u = - 1

4 u^{2} + 2 u = 2

2

を左側に移動します

4 u^{2} + 2 u = 2

両辺から

2

を引く

4 u^{2} + 2 u - 2 = 2 - 2

簡素化

4 u^{2} + 2 u - 2 = 0

4 u^{2} + 2 u - 2 = 0

解くとthe二次式

4 u^{2} + 2 u - 2 = 0

二次Equationの公式:

次の場合:

a = 4, b = 2, c = - 2

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 4 ( - 2 )}{2 \cdot 4}

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 4 ( - 2 )}{2 \cdot 4}

2^{2} - 4 \cdot 4 (- 2) = 6

2^{2} - 4 \cdot 4 (- 2)

規則を適用

- (- a) = a

= 2^{2} + 4 \cdot 4 \cdot 2

数を乗じる:

4 \cdot 4 \cdot 2 = 32

= 2^{2} + 32

2^{2} = 4

= 4 + 32

数を足す:

4 + 32 = 36

= 36

数を因数に分解する:

36 = 6^{2}

= 6^{2}

累乗根の規則を適用する:

n a^{n} = a

6^{2} = 6

= 6

u_{1, 2} = \frac{- 2 \pm 6}{2 \cdot 4}

解を分離する

u_{1} = \frac{- 2 + 6}{2 \cdot 4}, u_{2} = \frac{- 2 - 6}{2 \cdot 4}

u = \frac{- 2 + 6}{2 \cdot 4} : \frac{1}{2}

\frac{- 2 + 6}{2 \cdot 4}

数を足す/引く:

- 2 + 6 = 4

= \frac{4}{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= \frac{4}{8}

共通因数を約分する:

4

= \frac{1}{2}

u = \frac{- 2 - 6}{2 \cdot 4} : - 1

\frac{- 2 - 6}{2 \cdot 4}

数を引く:

- 2 - 6 = - 8

= \frac{- 8}{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= \frac{- 8}{8}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{8}{8}

規則を適用

\frac{a}{a} = 1

= - 1

二次equationの解:

u = \frac{1}{2}, u = - 1

代用を戻す

u = sin (x)

sin (x) = \frac{1}{2}, sin (x) = - 1

sin (x) = \frac{1}{2}, sin (x) = - 1

sin (x) = \frac{1}{2}, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{5 π}{6}

sin (x) = \frac{1}{2}, 0 \leq x \leq 2 π

以下の一般解

sin (x) = \frac{1}{2}

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}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

範囲の解答

0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{5 π}{6}

sin (x) = - 1, 0 \leq x \leq 2 π : x = \frac{3 π}{2}

sin (x) = - 1, 0 \leq x \leq 2 π

以下の一般解

sin (x) = - 1

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}

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

範囲の解答

0 \leq x \leq 2 π

x = \frac{3 π}{2}

すべての解を組み合わせる

x = \frac{π}{6}, x = \frac{5 π}{6}, x = \frac{3 π}{2}

グラフ

人気の例

3 tan (\frac{1}{3} x) = 8

1.65^2=0.65^2+1.77^2-2(0.65)(1.77)cos(A)

1.6 5^{2} = 0.6 5^{2} + 1.7 7^{2} - 2 (0.65) (1.77) cos (A)

solvefor x,cos(3x+pi/4)= 1/(sqrt(2))

so l v e f or x, cos (3 x + \frac{π}{4}) = \frac{1}{2}

solvefor x,cos^2(3x+pi/4)= 3/4

so l v e f or x, cos^{2} (3 x + \frac{π}{4}) = \frac{3}{4}

(tan(x^2+6)-1)/(tan(x))=0

\frac{tan ( x ^{2} + 6 ) - 1}{tan ( x )} = 0