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受欢迎的三角函数 >

sin^2(θ)=5sin(θ)+6

解答

sin^{2} (θ) = 5 sin (θ) + 6

解答

θ = \frac{3 π}{2} + 2 πn

+1

度数

θ = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (θ) = 5 sin (θ) + 6

用替代法求解

sin^{2} (θ) = 5 sin (θ) + 6

令

: sin (θ) = u

u^{2} = 5 u + 6

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

u^{2} = 5 u + 6

将

6

para o lado esquerdo

u^{2} = 5 u + 6

两边减去

6

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

化简

u^{2} - 6 = 5 u

u^{2} - 6 = 5 u

将

5 u

para o lado esquerdo

u^{2} - 6 = 5 u

两边减去

5 u

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

化简

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

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

改写成标准形式

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

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

使用求根公式求解

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

二次方程求根公式:

若

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

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

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

(- 5)^{2} - 4 \cdot 1 \cdot (- 6) = 7

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

使用法则

- (- a) = a

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

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 5)^{2} = 5^{2}

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

数字相乘:

4 \cdot 1 \cdot 6 = 24

= 5^{2} + 24

5^{2} = 25

= 25 + 24

数字相加:

25 + 24 = 49

= 49

因式分解数字:

49 = 7^{2}

= 7^{2}

使用根式运算法则:

n a^{n} = a

7^{2} = 7

= 7

u_{1, 2} = \frac{- ( - 5 ) \pm 7}{2 \cdot 1}

将解分隔开

u_{1} = \frac{- ( - 5 ) + 7}{2 \cdot 1}, u_{2} = \frac{- ( - 5 ) - 7}{2 \cdot 1}

u = \frac{- ( - 5 ) + 7}{2 \cdot 1} : 6

\frac{- ( - 5 ) + 7}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{5 + 7}{2 \cdot 1}

数字相加:

5 + 7 = 12

= \frac{12}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{12}{2}

数字相除:

\frac{12}{2} = 6

= 6

u = \frac{- ( - 5 ) - 7}{2 \cdot 1} : - 1

\frac{- ( - 5 ) - 7}{2 \cdot 1}

使用法则

- (- a) = a

= \frac{5 - 7}{2 \cdot 1}

数字相减:

5 - 7 = - 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

二次方程组的解是:

u = 6, u = - 1

u = sin (θ)

代回

sin (θ) = 6, sin (θ) = - 1

sin (θ) = 6, sin (θ) = - 1

sin (θ) = 6 :

无解

sin (θ) = 6

- 1 \leq sin (x) \leq 1

无解

sin (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

sin (θ) = - 1

sin (θ) = - 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}

θ = \frac{3 π}{2} + 2 πn

θ = \frac{3 π}{2} + 2 πn

合并所有解

θ = \frac{3 π}{2} + 2 πn

作图

流行的例子

2 = 2 sec (x)

cos(x)-sin(x)=(sqrt(2))/2

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

2/5 cos(x)=(sqrt(2))/5

\frac{2}{5} cos (x) = \frac{2}{5}

sin^2(x)=6(cos(-x)+1)

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

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

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