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受欢迎的三角函数 >

3sin^2(x)+6sin(x)+3=0

解答

3 sin^{2} (x) + 6 sin (x) + 3 = 0

解答

x = \frac{3 π}{2} + 2 πn

+1

度数

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

求解步骤

3 sin^{2} (x) + 6 sin (x) + 3 = 0

用替代法求解

3 sin^{2} (x) + 6 sin (x) + 3 = 0

令

: sin (x) = u

3 u^{2} + 6 u + 3 = 0

3 u^{2} + 6 u + 3 = 0 : u = - 1

3 u^{2} + 6 u + 3 = 0

使用求根公式求解

3 u^{2} + 6 u + 3 = 0

二次方程求根公式:

若

a = 3, b = 6, c = 3

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 3 \cdot 3}{2 \cdot 3}

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 3 \cdot 3}{2 \cdot 3}

6^{2} - 4 \cdot 3 \cdot 3 = 0

6^{2} - 4 \cdot 3 \cdot 3

数字相乘:

4 \cdot 3 \cdot 3 = 36

= 6^{2} - 36

6^{2} = 36

= 36 - 36

数字相减:

36 - 36 = 0

= 0

u_{1, 2} = \frac{- 6 \pm 0}{2 \cdot 3}

u = \frac{- 6}{2 \cdot 3}

\frac{- 6}{2 \cdot 3} = - 1

\frac{- 6}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 6}{6}

使用分式法则:

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

= - \frac{6}{6}

使用法则

\frac{a}{a} = 1

= - 1

u = - 1

二次方程组的解是:

u = - 1

u = sin (x)

代回

sin (x) = - 1

sin (x) = - 1

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

3sin(x)-4=sin(x)-2

3 sin (x) - 4 = sin (x) - 2

sin (θ) = - \frac{5}{6}

sec (θ) = 0

2sin^2(x)-cos(x)-1=0,0<= x<= 2pi

2 sin^{2} (x) - cos (x) - 1 = 0, 0 \leq x \leq 2 π

5tan(x)sin(x)=-sin(x)

5 tan (x) sin (x) = - sin (x)