zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

12sin^2(x)+8sin(x)+1=0

解答

12 sin^{2} (x) + 8 sin (x) + 1 = 0

解答

x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度数

x = - 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 189.59406 \dots^{\circ} + 36 0^{\circ} n, x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

12 sin^{2} (x) + 8 sin (x) + 1 = 0

用替代法求解

12 sin^{2} (x) + 8 sin (x) + 1 = 0

令

: sin (x) = u

12 u^{2} + 8 u + 1 = 0

12 u^{2} + 8 u + 1 = 0 : u = - \frac{1}{6}, u = - \frac{1}{2}

12 u^{2} + 8 u + 1 = 0

使用求根公式求解

12 u^{2} + 8 u + 1 = 0

二次方程求根公式:

若

a = 12, b = 8, c = 1

u_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 12 \cdot 1}{2 \cdot 12}

u_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 12 \cdot 1}{2 \cdot 12}

8^{2} - 4 \cdot 12 \cdot 1 = 4

8^{2} - 4 \cdot 12 \cdot 1

数字相乘:

4 \cdot 12 \cdot 1 = 48

= 8^{2} - 48

8^{2} = 64

= 64 - 48

数字相减:

64 - 48 = 16

= 16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

u_{1, 2} = \frac{- 8 \pm 4}{2 \cdot 12}

将解分隔开

u_{1} = \frac{- 8 + 4}{2 \cdot 12}, u_{2} = \frac{- 8 - 4}{2 \cdot 12}

u = \frac{- 8 + 4}{2 \cdot 12} : - \frac{1}{6}

\frac{- 8 + 4}{2 \cdot 12}

数字相加/相减:

- 8 + 4 = - 4

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

数字相乘:

2 \cdot 12 = 24

= \frac{- 4}{24}

使用分式法则:

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

= - \frac{4}{24}

约分:

4

= - \frac{1}{6}

u = \frac{- 8 - 4}{2 \cdot 12} : - \frac{1}{2}

\frac{- 8 - 4}{2 \cdot 12}

数字相减:

- 8 - 4 = - 12

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

数字相乘:

2 \cdot 12 = 24

= \frac{- 12}{24}

使用分式法则:

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

= - \frac{12}{24}

约分:

12

= - \frac{1}{2}

二次方程组的解是:

u = - \frac{1}{6}, u = - \frac{1}{2}

u = sin (x)

代回

sin (x) = - \frac{1}{6}, sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{6}, sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{6} : x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

sin (x) = - \frac{1}{6}

使用反三角函数性质

sin (x) = - \frac{1}{6}

sin (x) = - \frac{1}{6}

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

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

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{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

合并所有解

x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

以小数形式表示解

x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

作图

流行的例子

3*tan(x)+1=0,x,0<= x<= 2*pi

3 \cdot tan (x) + 1 = 0, x, 0 \leq x \leq 2 \cdot π

cot^2(x)-3cot(x)-4=0

cot^{2} (x) - 3 cot (x) - 4 = 0

cot (b) = 0.5008

1/(6tan^6(x))= 1/(6sec^6(x))

\frac{1}{6 tan ^{6} ( x )} = \frac{1}{6 sec ^{6} ( x )}

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

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