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 >

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

解答

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

两边减去

1 - cos (2 a)

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

使用三角恒等式改写

- 1 + cos (2 a) + sin^{2} (a)

使用倍角公式:

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

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

= - 1 + cos (2 a) - (cos (2 a) - cos^{2} (a))

化简

- 1 + cos (2 a) - (cos (2 a) - cos^{2} (a)) : - 1 + cos^{2} (a)

- 1 + cos (2 a) - (cos (2 a) - cos^{2} (a))

- (cos (2 a) - cos^{2} (a)) : - cos (2 a) + cos^{2} (a)

- (cos (2 a) - cos^{2} (a))

打开括号

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

使用加减运算法则

- (- a) = a, - (a) = - a

= - cos (2 a) + cos^{2} (a)

= - 1 + cos (2 a) - cos (2 a) + cos^{2} (a)

同类项相加:

cos (2 a) - cos (2 a) = 0

= - 1 + cos^{2} (a)

= - 1 + cos^{2} (a)

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

用替代法求解

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

令

: cos (a) = u

- 1 + u^{2} = 0

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

- 1 + u^{2} = 0

将

1

到右边

- 1 + u^{2} = 0

两边加上

1

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

化简

u^{2} = 1

u^{2} = 1

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 1, u = - 1

1 = 1

1

使用法则

1 = 1

= 1

- 1 = - 1

- 1

使用法则

1 = 1

= - 1

u = 1, u = - 1

u = cos (a)

代回

cos (a) = 1, cos (a) = - 1

cos (a) = 1, cos (a) = - 1

cos (a) = 1 : a = 2 πn

cos (a) = 1

cos (a) = 1

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

a = 0 + 2 πn

a = 0 + 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

cos (a) = - 1 : a = π + 2 πn

cos (a) = - 1

cos (a) = - 1

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

a = π + 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

cos^4(x)=cos^2(x)

cos^{4} (x) = cos^{2} (x)

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

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

2*sin(a)=sin(3a)

2 \cdot sin (a) = sin (3 a)

(cos(x)+5sin(x))/(2-3)=0

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

sin (y) = \frac{2}{3}