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受欢迎的三角函数 >

2sin^2(u)=1-sin(u)

解答

2 sin^{2} (u) = 1 - sin (u)

解答

u = \frac{π}{6} + 2 πn, u = \frac{5 π}{6} + 2 πn, u = \frac{3 π}{2} + 2 πn

+1

度数

u = 3 0^{\circ} + 36 0^{\circ} n, u = 15 0^{\circ} + 36 0^{\circ} n, u = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

2 sin^{2} (u) = 1 - sin (u)

用替代法求解

2 sin^{2} (u) = 1 - sin (u)

令

: sin (u) = v

2 v^{2} = 1 - v

2 v^{2} = 1 - v : v = \frac{1}{2}, v = - 1

2 v^{2} = 1 - v

将

v

para o lado esquerdo

2 v^{2} = 1 - v

两边加上

v

2 v^{2} + v = 1 - v + v

化简

2 v^{2} + v = 1

2 v^{2} + v = 1

将

1

para o lado esquerdo

2 v^{2} + v = 1

两边减去

1

2 v^{2} + v - 1 = 1 - 1

化简

2 v^{2} + v - 1 = 0

2 v^{2} + v - 1 = 0

使用求根公式求解

2 v^{2} + v - 1 = 0

二次方程求根公式:

若

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

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

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

1^{2} - 4 \cdot 2 (- 1) = 3

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

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 2 (- 1)

使用法则

- (- a) = a

= 1 + 4 \cdot 2 \cdot 1

数字相乘:

4 \cdot 2 \cdot 1 = 8

= 1 + 8

数字相加:

1 + 8 = 9

= 9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

v_{1, 2} = \frac{- 1 \pm 3}{2 \cdot 2}

将解分隔开

v_{1} = \frac{- 1 + 3}{2 \cdot 2}, v_{2} = \frac{- 1 - 3}{2 \cdot 2}

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

\frac{- 1 + 3}{2 \cdot 2}

数字相加/相减:

- 1 + 3 = 2

= \frac{2}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{2}{4}

约分:

2

= \frac{1}{2}

v = \frac{- 1 - 3}{2 \cdot 2} : - 1

\frac{- 1 - 3}{2 \cdot 2}

数字相减:

- 1 - 3 = - 4

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 4}{4}

使用分式法则:

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

= - \frac{4}{4}

使用法则

\frac{a}{a} = 1

= - 1

二次方程组的解是:

v = \frac{1}{2}, v = - 1

v = sin (u)

代回

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

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

sin (u) = \frac{1}{2} : u = \frac{π}{6} + 2 πn, u = \frac{5 π}{6} + 2 πn

sin (u) = \frac{1}{2}

sin (u) = \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}

u = \frac{π}{6} + 2 πn, u = \frac{5 π}{6} + 2 πn

u = \frac{π}{6} + 2 πn, u = \frac{5 π}{6} + 2 πn

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

sin (u) = - 1

sin (u) = - 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}

u = \frac{3 π}{2} + 2 πn

u = \frac{3 π}{2} + 2 πn

合并所有解

u = \frac{π}{6} + 2 πn, u = \frac{5 π}{6} + 2 πn, u = \frac{3 π}{2} + 2 πn

作图

流行的例子

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

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

sin(t)=-(sqrt(3))/2

sin (t) = - \frac{3}{2}

2sin(2θ)-3sin(θ)=0

2 sin (2 θ) - 3 sin (θ) = 0

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

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

4cos^2(x)-1=0,0<= x<= 2pi

4 cos^{2} (x) - 1 = 0, 0 \leq x \leq 2 π