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 >

-8cos^2(x)+6=2

解答

- 8 cos^{2} (x) + 6 = 2

解答

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

+1

度数

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = - 13 5^{\circ} + 36 0^{\circ} n

求解步骤

- 8 cos^{2} (x) + 6 = 2

用替代法求解

- 8 cos^{2} (x) + 6 = 2

令

: cos (x) = u

- 8 u^{2} + 6 = 2

- 8 u^{2} + 6 = 2 : u = \frac{1}{2}, u = - \frac{1}{2}

- 8 u^{2} + 6 = 2

将

6

到右边

- 8 u^{2} + 6 = 2

两边减去

6

- 8 u^{2} + 6 - 6 = 2 - 6

化简

- 8 u^{2} = - 4

- 8 u^{2} = - 4

两边除以

- 8

- 8 u^{2} = - 4

两边除以

- 8

\frac{- 8 u ^{2}}{- 8} = \frac{- 4}{- 8}

化简

\frac{- 8 u ^{2}}{- 8} = \frac{- 4}{- 8}

化简

\frac{- 8 u ^{2}}{- 8} : u^{2}

\frac{- 8 u ^{2}}{- 8}

使用分式法则:

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

= \frac{8 u ^{2}}{8}

数字相除:

\frac{8}{8} = 1

= u^{2}

化简

\frac{- 4}{- 8} : \frac{1}{2}

\frac{- 4}{- 8}

使用分式法则:

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

= \frac{4}{8}

约分:

4

= \frac{1}{2}

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2}

对于

x^{2} = f (a)

解为

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

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

u = cos (x)

代回

cos (x) = \frac{1}{2}, cos (x) = - \frac{1}{2}

cos (x) = \frac{1}{2}, cos (x) = - \frac{1}{2}

cos (x) = \frac{1}{2} : x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn

cos (x) = \frac{1}{2}

使用反三角函数性质

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

的通解

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

x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn

x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn

cos (x) = - \frac{1}{2} : x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

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

使用反三角函数性质

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

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

的通解

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

x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

合并所有解

x = arccos (\frac{1}{2}) + 2 πn, x = 2 π - arccos (\frac{1}{2}) + 2 πn, x = arccos (- \frac{1}{2}) + 2 πn, x = - arccos (- \frac{1}{2}) + 2 πn

以小数形式表示解

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

作图

流行的例子

sin (x) = \frac{10}{20}

(sin(x)+cos(x))/(sin(x))=1-1/(tan(x))

\frac{sin ( x ) + cos ( x )}{sin ( x )} = 1 - \frac{1}{tan ( x )}

6cos^2(x)-5sin(x)-2=0

6 cos^{2} (x) - 5 sin (x) - 2 = 0

sec (θ) = - \frac{7}{4}

arctan(x)=infinity

arctan (x) = \infty