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(x)+3cos(x)-2=0

解答

2 cos (x) + 3 cos (x) - 2 = 0

解答

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

+1

度数

x = 66.42182 \dots^{\circ} + 36 0^{\circ} n, x = 293.57817 \dots^{\circ} + 36 0^{\circ} n

求解步骤

2 cos (x) + 3 cos (x) - 2 = 0

化简

2 cos (x) + 3 cos (x) - 2 : 5 cos (x) - 2

2 cos (x) + 3 cos (x) - 2

同类项相加:

2 cos (x) + 3 cos (x) = 5 cos (x)

= 5 cos (x) - 2

5 cos (x) - 2 = 0

将

2

到右边

5 cos (x) - 2 = 0

两边加上

2

5 cos (x) - 2 + 2 = 0 + 2

化简

5 cos (x) = 2

5 cos (x) = 2

两边除以

5

5 cos (x) = 2

两边除以

5

\frac{5 cos ( x )}{5} = \frac{2}{5}

化简

cos (x) = \frac{2}{5}

cos (x) = \frac{2}{5}

使用反三角函数性质

cos (x) = \frac{2}{5}

cos (x) = \frac{2}{5}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn

x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn

以小数形式表示解

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

作图

流行的例子

sec((5θ)/4)=2,[0.2pi]

cos(x)+|cos(x)|=1,-2pi<= x<= 2pi

(30.56)/(sin(88))=(17)/(sin(x))

sec(x+pi/4)=-sqrt(2),-pi<= x<= pi

(56)/((7.071*7.681))=cos(θ)