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 >

9cos^2(x)=2

解答

9 cos^{2} (x) = 2

解答

x = 1.07991 \dots + 2 πn, x = 2 π - 1.07991 \dots + 2 πn, x = 2.06167 \dots + 2 πn, x = - 2.06167 \dots + 2 πn

+1

度数

x = 61.87449 \dots^{\circ} + 36 0^{\circ} n, x = 298.12550 \dots^{\circ} + 36 0^{\circ} n, x = 118.12550 \dots^{\circ} + 36 0^{\circ} n, x = - 118.12550 \dots^{\circ} + 36 0^{\circ} n

求解步骤

9 cos^{2} (x) = 2

用替代法求解

9 cos^{2} (x) = 2

令

: cos (x) = u

9 u^{2} = 2

9 u^{2} = 2 : u = \frac{2}{3}, u = - \frac{2}{3}

9 u^{2} = 2

两边除以

9

9 u^{2} = 2

两边除以

9

\frac{9 u ^{2}}{9} = \frac{2}{9}

化简

u^{2} = \frac{2}{9}

u^{2} = \frac{2}{9}

对于

x^{2} = f (a)

解为

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

u = \frac{2}{9}, u = - \frac{2}{9}

\frac{2}{9} = \frac{2}{3}

\frac{2}{9}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{2}{9}

9 = 3

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

= \frac{2}{3}

- \frac{2}{9} = - \frac{2}{3}

- \frac{2}{9}

化简

\frac{2}{9} : \frac{2}{3}

\frac{2}{9}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{2}{9}

9 = 3

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

= \frac{2}{3}

= - \frac{2}{3}

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

u = cos (x)

代回

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

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

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

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

使用反三角函数性质

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

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

的通解

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

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

cos (x) = - \frac{2}{3} : x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

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

使用反三角函数性质

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

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

的通解

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

x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

合并所有解

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn, x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

以小数形式表示解

x = 1.07991 \dots + 2 πn, x = 2 π - 1.07991 \dots + 2 πn, x = 2.06167 \dots + 2 πn, x = - 2.06167 \dots + 2 πn

作图

流行的例子

tan (θ) = \frac{6}{14}

tan (θ) = \frac{6}{15}

tan (x) = \frac{10}{3}

csc^2(x)-csc(x)-2=0,-pi<= x<= pi

csc^{2} (x) - csc (x) - 2 = 0, - π \leq x \leq π

solvefor θ,r=vcos(θ)((2vsin(θ))/g)

so l v e f or θ, r = v cos (θ) (\frac{2 v sin ( θ )}{g})