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受欢迎的三角函数 >

sin^2(x)+6sin(x)=2sin(x)-3

解答

sin^{2} (x) + 6 sin (x) = 2 sin (x) - 3

解答

x = \frac{3 π}{2} + 2 πn

+1

度数

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

求解步骤

sin^{2} (x) + 6 sin (x) = 2 sin (x) - 3

用替代法求解

sin^{2} (x) + 6 sin (x) = 2 sin (x) - 3

令

: sin (x) = u

u^{2} + 6 u = 2 u - 3

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

u^{2} + 6 u = 2 u - 3

将

3

para o lado esquerdo

u^{2} + 6 u = 2 u - 3

两边加上

3

u^{2} + 6 u + 3 = 2 u - 3 + 3

化简

u^{2} + 6 u + 3 = 2 u

u^{2} + 6 u + 3 = 2 u

将

2 u

para o lado esquerdo

u^{2} + 6 u + 3 = 2 u

两边减去

2 u

u^{2} + 6 u + 3 - 2 u = 2 u - 2 u

化简

u^{2} + 4 u + 3 = 0

u^{2} + 4 u + 3 = 0

使用求根公式求解

u^{2} + 4 u + 3 = 0

二次方程求根公式:

若

a = 1, b = 4, c = 3

u_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

u_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

4^{2} - 4 \cdot 1 \cdot 3 = 2

4^{2} - 4 \cdot 1 \cdot 3

数字相乘:

4 \cdot 1 \cdot 3 = 12

= 4^{2} - 12

4^{2} = 16

= 16 - 12

数字相减:

16 - 12 = 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{- 4 \pm 2}{2 \cdot 1}

将解分隔开

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

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

\frac{- 4 + 2}{2 \cdot 1}

数字相加/相减:

- 4 + 2 = - 2

= \frac{- 2}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 2}{2}

使用分式法则:

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

= - \frac{2}{2}

使用法则

\frac{a}{a} = 1

= - 1

u = \frac{- 4 - 2}{2 \cdot 1} : - 3

\frac{- 4 - 2}{2 \cdot 1}

数字相减:

- 4 - 2 = - 6

= \frac{- 6}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 6}{2}

使用分式法则:

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

= - \frac{6}{2}

数字相除:

\frac{6}{2} = 3

= - 3

二次方程组的解是:

u = - 1, u = - 3

u = sin (x)

代回

sin (x) = - 1, sin (x) = - 3

sin (x) = - 1, sin (x) = - 3

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

sin (x) = - 3 :

无解

sin (x) = - 3

- 1 \leq sin (x) \leq 1

无解

合并所有解

x = \frac{3 π}{2} + 2 πn

作图

流行的例子

sin(x)+cos(x)= 1/5

sin (x) + cos (x) = \frac{1}{5}

cos((2x)/3)-1=0

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

4sin^2(θ)-11sin(θ)+7=0

4 sin^{2} (θ) - 11 sin (θ) + 7 = 0

cos^2(x)+cos^4(x)=1

cos^{2} (x) + cos^{4} (x) = 1

- 3 cos (θ) = 2