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受欢迎的三角函数 >

-4cos^2(x)+6cos(x)=2

解答

- 4 cos^{2} (x) + 6 cos (x) = 2

解答

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

+1

度数

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

求解步骤

- 4 cos^{2} (x) + 6 cos (x) = 2

用替代法求解

- 4 cos^{2} (x) + 6 cos (x) = 2

令

: cos (x) = u

- 4 u^{2} + 6 u = 2

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

- 4 u^{2} + 6 u = 2

将

2

para o lado esquerdo

- 4 u^{2} + 6 u = 2

两边减去

2

- 4 u^{2} + 6 u - 2 = 2 - 2

化简

- 4 u^{2} + 6 u - 2 = 0

- 4 u^{2} + 6 u - 2 = 0

使用求根公式求解

- 4 u^{2} + 6 u - 2 = 0

二次方程求根公式:

若

a = - 4, b = 6, c = - 2

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 4 ) ( - 2 )}{2 ( - 4 )}

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 4 ) ( - 2 )}{2 ( - 4 )}

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

6^{2} - 4 (- 4) (- 2)

使用法则

- (- a) = a

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

数字相乘:

4 \cdot 4 \cdot 2 = 32

= 6^{2} - 32

6^{2} = 36

= 36 - 32

数字相减:

36 - 32 = 4

= 4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

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

将解分隔开

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

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

\frac{- 6 + 2}{2 ( - 4 )}

去除括号:

(- a) = - a

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

数字相加/相减:

- 6 + 2 = - 4

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

数字相乘:

2 \cdot 4 = 8

= \frac{- 4}{- 8}

使用分式法则:

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

= \frac{4}{8}

约分:

4

= \frac{1}{2}

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

\frac{- 6 - 2}{2 ( - 4 )}

去除括号:

(- a) = - a

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

数字相减:

- 6 - 2 = - 8

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

数字相乘:

2 \cdot 4 = 8

= \frac{- 8}{- 8}

使用分式法则:

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

= \frac{8}{8}

使用法则

\frac{a}{a} = 1

= 1

二次方程组的解是:

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

u = cos (x)

代回

cos (x) = \frac{1}{2}, cos (x) = 1

cos (x) = \frac{1}{2}, cos (x) = 1

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

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

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

的通解

cos (x)

周期表（周期为

2 πn

）：

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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

cos (x) = 1 : x = 2 πn

cos (x) = 1

cos (x) = 1

的通解

cos (x)

周期表（周期为

2 πn

）：

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 = 0 + 2 πn

x = 0 + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

合并所有解

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

作图

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1.33 \cdot sin (5 6^{\circ}) = 1 \cdot sin (x)