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受欢迎的三角函数 >

4+4cos(x)=-6cos(x)

解答

4 + 4 cos (x) = - 6 cos (x)

解答

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

+1

度数

x = 113.57817 \dots^{\circ} + 36 0^{\circ} n, x = - 113.57817 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4 + 4 cos (x) = - 6 cos (x)

用替代法求解

4 + 4 cos (x) = - 6 cos (x)

令

: cos (x) = u

4 + 4 u = - 6 u

4 + 4 u = - 6 u : u = - \frac{2}{5}

4 + 4 u = - 6 u

将

4

到右边

4 + 4 u = - 6 u

两边减去

4

4 + 4 u - 4 = - 6 u - 4

化简

4 u = - 6 u - 4

4 u = - 6 u - 4

将

6 u

para o lado esquerdo

4 u = - 6 u - 4

两边加上

6 u

4 u + 6 u = - 6 u - 4 + 6 u

化简

10 u = - 4

10 u = - 4

两边除以

10

10 u = - 4

两边除以

10

\frac{10 u}{10} = \frac{- 4}{10}

化简

\frac{10 u}{10} = \frac{- 4}{10}

化简

\frac{10 u}{10} : u

\frac{10 u}{10}

数字相除:

\frac{10}{10} = 1

= u

化简

\frac{- 4}{10} : - \frac{2}{5}

\frac{- 4}{10}

使用分式法则:

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

= - \frac{4}{10}

约分:

2

= - \frac{2}{5}

u = - \frac{2}{5}

u = - \frac{2}{5}

u = - \frac{2}{5}

u = cos (x)

代回

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

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

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

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 = - arccos (- a) + 2 πn

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

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

合并所有解

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

以小数形式表示解

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

作图

流行的例子

2cos(x/2)=sqrt(3),0<= x<= 2pi

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

sin (A) = \frac{4}{5}

3tan^2(x)-1=0,0<= x<= 2pi

3 tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

sin(2x)=4cos(x)

sin (2 x) = 4 cos (x)

sqrt(3)tan(2x)-1=0

3 tan (2 x) - 1 = 0