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受欢迎的三角函数 >

sin^2(x)+2sin(x)=-1

解答

sin^{2} (x) + 2 sin (x) = - 1

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) + 2 sin (x) = - 1

用替代法求解

sin^{2} (x) + 2 sin (x) = - 1

令

: sin (x) = u

u^{2} + 2 u = - 1

u^{2} + 2 u = - 1 : u = - 1

u^{2} + 2 u = - 1

将

1

para o lado esquerdo

u^{2} + 2 u = - 1

两边加上

1

u^{2} + 2 u + 1 = - 1 + 1

化简

u^{2} + 2 u + 1 = 0

u^{2} + 2 u + 1 = 0

使用求根公式求解

u^{2} + 2 u + 1 = 0

二次方程求根公式:

若

a = 1, b = 2, c = 1

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

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

2^{2} - 4 \cdot 1 \cdot 1 = 0

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

数字相乘:

4 \cdot 1 \cdot 1 = 4

= 2^{2} - 4

2^{2} = 4

= 4 - 4

数字相减:

4 - 4 = 0

= 0

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

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

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

\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 = - 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

cos(2x)=11sin(x)-5

cos (2 x) = 11 sin (x) - 5

solvefor x,z= 4/pi arctan(xy)

so l v e f or x, z = \frac{4}{π} arctan (x y)

solvefor x,cos(2x)+sin(x)=0

so l v e f or x, cos (2 x) + sin (x) = 0

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

|cos(x/4)|= 1/2

cos (\frac{x}{4}) = \frac{1}{2}