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受欢迎的三角函数 >

sin^2(a)=2sin(a)

解答

sin^{2} (a) = 2 sin (a)

解答

a = 2 πn, a = π + 2 πn

+1

度数

a = 0^{\circ} + 36 0^{\circ} n, a = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (a) = 2 sin (a)

用替代法求解

sin^{2} (a) = 2 sin (a)

令

: sin (a) = u

u^{2} = 2 u

u^{2} = 2 u : u = 2, u = 0

u^{2} = 2 u

将

2 u

para o lado esquerdo

u^{2} = 2 u

两边减去

2 u

u^{2} - 2 u = 2 u - 2 u

化简

u^{2} - 2 u = 0

u^{2} - 2 u = 0

使用求根公式求解

u^{2} - 2 u = 0

二次方程求根公式:

若

a = 1, b = - 2, c = 0

u_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

u_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot 0 = 2

(- 2)^{2} - 4 \cdot 1 \cdot 0

使用指数法则:

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

若

n

是偶数

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

= 2^{2} - 4 \cdot 1 \cdot 0

使用法则

0 \cdot a = 0

= 2^{2} - 0

2^{2} - 0 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 2

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

将解分隔开

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

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

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

使用法则

- (- a) = a

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

数字相加:

2 + 2 = 4

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

数字相乘:

2 \cdot 1 = 2

= \frac{4}{2}

数字相除:

\frac{4}{2} = 2

= 2

u = \frac{- ( - 2 ) - 2}{2 \cdot 1} : 0

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

使用法则

- (- a) = a

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

数字相减:

2 - 2 = 0

= \frac{0}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{0}{2}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

二次方程组的解是:

u = 2, u = 0

u = sin (a)

代回

sin (a) = 2, sin (a) = 0

sin (a) = 2, sin (a) = 0

sin (a) = 2 :

无解

sin (a) = 2

- 1 \leq sin (x) \leq 1

无解

sin (a) = 0 : a = 2 πn, a = π + 2 πn

sin (a) = 0

sin (a) = 0

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}

a = 0 + 2 πn, a = π + 2 πn

a = 0 + 2 πn, a = π + 2 πn

解

a = 0 + 2 πn : a = 2 πn

a = 0 + 2 πn

0 + 2 πn = 2 πn

a = 2 πn

a = 2 πn, a = π + 2 πn

合并所有解

a = 2 πn, a = π + 2 πn

作图

流行的例子

sin(3x-50)cos(x)-cos(3x-50)sin(x)=0,0<= x<= 180

sin (3 x - 50) cos (x) - cos (3 x - 50) sin (x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

10 cos^{2} (x) = 9

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

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

0.5 cos (x) = 0

(sin(x))/5 =(sin(125))/(20)

\frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}