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 >

cos^2(x)+6sin(x)-6=0

解答

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

解答

x = \frac{π}{2} + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n

求解步骤

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

使用三角恒等式改写

- 6 + cos^{2} (x) + 6 sin (x)

使用毕达哥拉斯恒等式:

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

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

= - 6 + 1 - sin^{2} (x) + 6 sin (x)

化简

= 6 sin (x) - sin^{2} (x) - 5

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

用替代法求解

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

令

: sin (x) = u

- 5 - u^{2} + 6 u = 0

- 5 - u^{2} + 6 u = 0 : u = 1, u = 5

- 5 - u^{2} + 6 u = 0

改写成标准形式

a x^{2} + b x + c = 0

- u^{2} + 6 u - 5 = 0

使用求根公式求解

- u^{2} + 6 u - 5 = 0

二次方程求根公式:

若

a = - 1, b = 6, c = - 5

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 1 ) ( - 5 )}{2 ( - 1 )}

u_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 1 ) ( - 5 )}{2 ( - 1 )}

6^{2} - 4 (- 1) (- 5) = 4

6^{2} - 4 (- 1) (- 5)

使用法则

- (- a) = a

= 6^{2} - 4 \cdot 1 \cdot 5

数字相乘:

4 \cdot 1 \cdot 5 = 20

= 6^{2} - 20

6^{2} = 36

= 36 - 20

数字相减:

36 - 20 = 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{- 6 \pm 4}{2 ( - 1 )}

将解分隔开

u_{1} = \frac{- 6 + 4}{2 ( - 1 )}, u_{2} = \frac{- 6 - 4}{2 ( - 1 )}

u = \frac{- 6 + 4}{2 ( - 1 )} : 1

\frac{- 6 + 4}{2 ( - 1 )}

去除括号:

(- a) = - a

= \frac{- 6 + 4}{- 2 \cdot 1}

数字相加/相减:

- 6 + 4 = - 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{- 6 - 4}{2 ( - 1 )} : 5

\frac{- 6 - 4}{2 ( - 1 )}

去除括号:

(- a) = - a

= \frac{- 6 - 4}{- 2 \cdot 1}

数字相减:

- 6 - 4 = - 10

= \frac{- 10}{- 2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{- 10}{- 2}

使用分式法则:

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

= \frac{10}{2}

数字相除:

\frac{10}{2} = 5

= 5

二次方程组的解是:

u = 1, u = 5

u = sin (x)

代回

sin (x) = 1, sin (x) = 5

sin (x) = 1, sin (x) = 5

sin (x) = 1 : x = \frac{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{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

sin (x) = 5 :

无解

sin (x) = 5

- 1 \leq sin (x) \leq 1

无解

合并所有解

x = \frac{π}{2} + 2 πn

作图

流行的例子

(1-sin(x))*cos^3(x)=0

(1 - sin (x)) \cdot cos^{3} (x) = 0

- tan (x) = 3.465

3cos^2(x)-sin(x)+1=0

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

cos^2(x)+sin^2(x)+sin(x)= 1/2

cos^{2} (x) + sin^{2} (x) + sin (x) = \frac{1}{2}

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

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