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受欢迎的三角函数 >

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

解答

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

解答

x \in R 无解

求解步骤

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

用替代法求解

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

令

: sin (x) = u

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

2 u^{2} + u - 3 = 0 : u = 1, u = - \frac{3}{2}

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

使用求根公式求解

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

二次方程求根公式:

若

a = 2, b = 1, c = - 3

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

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

1^{2} - 4 \cdot 2 (- 3) = 5

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

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 2 (- 3)

使用法则

- (- a) = a

= 1 + 4 \cdot 2 \cdot 3

数字相乘:

4 \cdot 2 \cdot 3 = 24

= 1 + 24

数字相加:

1 + 24 = 25

= 25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

u_{1, 2} = \frac{- 1 \pm 5}{2 \cdot 2}

将解分隔开

u_{1} = \frac{- 1 + 5}{2 \cdot 2}, u_{2} = \frac{- 1 - 5}{2 \cdot 2}

u = \frac{- 1 + 5}{2 \cdot 2} : 1

\frac{- 1 + 5}{2 \cdot 2}

数字相加/相减:

- 1 + 5 = 4

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

数字相乘:

2 \cdot 2 = 4

= \frac{4}{4}

使用法则

\frac{a}{a} = 1

= 1

u = \frac{- 1 - 5}{2 \cdot 2} : - \frac{3}{2}

\frac{- 1 - 5}{2 \cdot 2}

数字相减:

- 1 - 5 = - 6

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 6}{4}

使用分式法则:

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

= - \frac{6}{4}

约分:

2

= - \frac{3}{2}

二次方程组的解是:

u = 1, u = - \frac{3}{2}

u = sin (x)

代回

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

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

sin (x) = 1, 6 :

无解

sin (x) = 1, 6

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{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

在

6

范围内的解

无解

sin (x) = - \frac{3}{2}, 6 :

无解

sin (x) = - \frac{3}{2}, 6

- 1 \leq sin (x) \leq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

(1-sin(2x))*(1-cos^2(x))=0

(1 - sin (2 x)) \cdot (1 - cos^{2} (x)) = 0

5cos(x)-10sin(x)cos(x)=0,0<= x<= pi/2

5 cos (x) - 10 sin (x) cos (x) = 0, 0 \leq x \leq \frac{π}{2}

|(211)||(-37-1)|(cos(x))=0

∣ (211) ∣ ∣ (- 37 - 1) ∣ (cos (x)) = 0

solvefor u,x=4sinh(u)

so l v e f or u, x = 4 sinh (u)

tan (x) = \frac{25}{32}