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受欢迎的三角函数 >

sin^2(θ)+2sin(θ)-15=0

解答

sin^{2} (θ) + 2 sin (θ) - 15 = 0

解答

θ \in R 无解

求解步骤

sin^{2} (θ) + 2 sin (θ) - 15 = 0

用替代法求解

sin^{2} (θ) + 2 sin (θ) - 15 = 0

令

: sin (θ) = u

u^{2} + 2 u - 15 = 0

u^{2} + 2 u - 15 = 0 : u = 3, u = - 5

u^{2} + 2 u - 15 = 0

使用求根公式求解

u^{2} + 2 u - 15 = 0

二次方程求根公式:

若

a = 1, b = 2, c = - 15

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 1 \cdot ( - 15 )}{2 \cdot 1}

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 1 \cdot ( - 15 )}{2 \cdot 1}

2^{2} - 4 \cdot 1 \cdot (- 15) = 8

2^{2} - 4 \cdot 1 \cdot (- 15)

使用法则

- (- a) = a

= 2^{2} + 4 \cdot 1 \cdot 15

数字相乘:

4 \cdot 1 \cdot 15 = 60

= 2^{2} + 60

2^{2} = 4

= 4 + 60

数字相加:

4 + 60 = 64

= 64

因式分解数字:

64 = 8^{2}

= 8^{2}

使用根式运算法则:

n a^{n} = a

8^{2} = 8

= 8

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

将解分隔开

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

u = \frac{- 2 + 8}{2 \cdot 1} : 3

\frac{- 2 + 8}{2 \cdot 1}

数字相加/相减:

- 2 + 8 = 6

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

数字相乘:

2 \cdot 1 = 2

= \frac{6}{2}

数字相除:

\frac{6}{2} = 3

= 3

u = \frac{- 2 - 8}{2 \cdot 1} : - 5

\frac{- 2 - 8}{2 \cdot 1}

数字相减:

- 2 - 8 = - 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 = 3, u = - 5

u = sin (θ)

代回

sin (θ) = 3, sin (θ) = - 5

sin (θ) = 3, sin (θ) = - 5

sin (θ) = 3 :

无解

sin (θ) = 3

- 1 \leq sin (x) \leq 1

无解

sin (θ) = - 5 :

无解

sin (θ) = - 5

- 1 \leq sin (x) \leq 1

无解

合并所有解

θ \in R 无解

作图

流行的例子

sin^2(x)+cos(x)= 5/4

sin^{2} (x) + cos (x) = \frac{5}{4}

cos(2θ)+2=5sin(θ)

cos (2 θ) + 2 = 5 sin (θ)

tan(x)-sin(2x)=0

tan (x) - sin (2 x) = 0

csc (2 x) = 0

3 sin (x + 4 5^{\circ}) = 2