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 >

2cos^2(x)=sqrt(3)*cos(x)

解答

2 cos^{2} (x) = 3 \cdot cos (x)

解答

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

2 cos^{2} (x) = 3 cos (x)

用替代法求解

2 cos^{2} (x) = 3 cos (x)

令

: cos (x) = u

2 u^{2} = 3 u

2 u^{2} = 3 u : u = 0, u = \frac{3}{2}

2 u^{2} = 3 u

将

3 u

para o lado esquerdo

2 u^{2} = 3 u

两边减去

3 u

2 u^{2} - 3 u = 3 u - 3 u

化简

2 u^{2} - 3 u = 0

2 u^{2} - 3 u = 0

因式分解

2 u^{2} - 3 u : u (2 u - 3)

2 u^{2} - 3 u

使用指数法则:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= 2 uu - 3 u

因式分解出通项

u

= u (2 u - 1 \cdot 2 3)

数字相乘:

1 \cdot 2 = 2

= u (2 u - 3)

u (2 u - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

u = 0 or 2 u - 3 = 0

解

2 u - 3 = 0 : u = \frac{3}{2}

2 u - 3 = 0

将

3

到右边

2 u - 3 = 0

两边加上

3

2 u - 3 + 3 = 0 + 3

化简

2 u = 3

2 u = 3

两边除以

2

2 u = 3

两边除以

2

\frac{2 u}{2} = \frac{3}{2}

化简

u = \frac{3}{2}

u = \frac{3}{2}

二次方程组的解是:

u = 0, u = \frac{3}{2}

u = cos (x)

代回

cos (x) = 0, cos (x) = \frac{3}{2}

cos (x) = 0, cos (x) = \frac{3}{2}

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

cos (x) = 0

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}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = \frac{3}{2} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

cos (x) = \frac{3}{2}

cos (x) = \frac{3}{2}

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}

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

合并所有解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

作图

流行的例子

4(cos(x)+1)cos(x)=3

4 (cos (x) + 1) cos (x) = 3

sin^2(x)+1=cos^2(x)-2sin^4(x)

sin^{2} (x) + 1 = cos^{2} (x) - 2 sin^{4} (x)

tan^{2} (x) - 1 = 2

cos(2a)= 2/3 ,sin(a)

cos (2 a) = \frac{2}{3}, sin (a)

cot (2 x - 3) - 1 = 0