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受欢迎的三角函数 >

4sin^2(x)=2sin(x)+6

解答

4 sin^{2} (x) = 2 sin (x) + 6

解答

x = \frac{3 π}{2} + 2 πn

+1

度数

x = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

4 sin^{2} (x) = 2 sin (x) + 6

用替代法求解

4 sin^{2} (x) = 2 sin (x) + 6

令

: sin (x) = u

4 u^{2} = 2 u + 6

4 u^{2} = 2 u + 6 : u = \frac{3}{2}, u = - 1

4 u^{2} = 2 u + 6

将

6

para o lado esquerdo

4 u^{2} = 2 u + 6

两边减去

6

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

化简

4 u^{2} - 6 = 2 u

4 u^{2} - 6 = 2 u

将

2 u

para o lado esquerdo

4 u^{2} - 6 = 2 u

两边减去

2 u

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

化简

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

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

改写成标准形式

a x^{2} + b x + c = 0

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

使用求根公式求解

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

二次方程求根公式:

若

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

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

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

(- 2)^{2} - 4 \cdot 4 (- 6) = 10

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

使用法则

- (- a) = a

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

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

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

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

数字相乘:

4 \cdot 4 \cdot 6 = 96

= 2^{2} + 96

2^{2} = 4

= 4 + 96

数字相加:

4 + 96 = 100

= 100

因式分解数字:

100 = 1 0^{2}

= 1 0^{2}

使用根式运算法则:

n a^{n} = a

1 0^{2} = 10

= 10

u_{1, 2} = \frac{- ( - 2 ) \pm 10}{2 \cdot 4}

将解分隔开

u_{1} = \frac{- ( - 2 ) + 10}{2 \cdot 4}, u_{2} = \frac{- ( - 2 ) - 10}{2 \cdot 4}

u = \frac{- ( - 2 ) + 10}{2 \cdot 4} : \frac{3}{2}

\frac{- ( - 2 ) + 10}{2 \cdot 4}

使用法则

- (- a) = a

= \frac{2 + 10}{2 \cdot 4}

数字相加:

2 + 10 = 12

= \frac{12}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{12}{8}

约分:

4

= \frac{3}{2}

u = \frac{- ( - 2 ) - 10}{2 \cdot 4} : - 1

\frac{- ( - 2 ) - 10}{2 \cdot 4}

使用法则

- (- a) = a

= \frac{2 - 10}{2 \cdot 4}

数字相减:

2 - 10 = - 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{3}{2}, u = - 1

u = sin (x)

代回

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

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

sin (x) = \frac{3}{2} :

无解

sin (x) = \frac{3}{2}

- 1 \leq sin (x) \leq 1

无解

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = - 1

sin (x) = - 1

的通解

sin (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} 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

合并所有解

x = \frac{3 π}{2} + 2 πn

作图

流行的例子

4 sin (x) - 1 = 0

cos (8 x) = - \frac{1}{2}

sqrt(2)sin(2x)=1,0<= x<= 2pi

2 sin (2 x) = 1, 0 \leq x \leq 2 π

cos (2 x) = 4

-sin(θ)-sin(2θ)=0

- sin (θ) - sin (2 θ) = 0