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 >

6sin(x)+2cos(x)=0

解答

6 sin (x) + 2 cos (x) = 0

解答

x = - 0.32175 \dots + πn

+1

度数

x = - 18.43494 \dots^{\circ} + 18 0^{\circ} n

求解步骤

6 sin (x) + 2 cos (x) = 0

使用三角恒等式改写

6 sin (x) + 2 cos (x) = 0

在两边除以

cos (x), cos (x) \neq = 0

\frac{6 sin ( x ) + 2 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

化简

\frac{6 sin ( x )}{cos ( x )} + 2 = 0

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

6 tan (x) + 2 = 0

6 tan (x) + 2 = 0

将

2

到右边

6 tan (x) + 2 = 0

两边减去

2

6 tan (x) + 2 - 2 = 0 - 2

化简

6 tan (x) = - 2

6 tan (x) = - 2

两边除以

6

6 tan (x) = - 2

两边除以

6

\frac{6 tan ( x )}{6} = \frac{- 2}{6}

化简

\frac{6 tan ( x )}{6} = \frac{- 2}{6}

化简

\frac{6 tan ( x )}{6} : tan (x)

\frac{6 tan ( x )}{6}

数字相除:

\frac{6}{6} = 1

= tan (x)

化简

\frac{- 2}{6} : - \frac{1}{3}

\frac{- 2}{6}

使用分式法则:

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

= - \frac{2}{6}

约分:

2

= - \frac{1}{3}

tan (x) = - \frac{1}{3}

tan (x) = - \frac{1}{3}

tan (x) = - \frac{1}{3}

使用反三角函数性质

tan (x) = - \frac{1}{3}

tan (x) = - \frac{1}{3}

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{1}{3}) + πn

x = arctan (- \frac{1}{3}) + πn

以小数形式表示解

x = - 0.32175 \dots + πn

作图

流行的例子

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

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

tan (θ) = \frac{5}{2}

sin^2(θ)=7(cos(-θ)+1)

sin^{2} (θ) = 7 (cos (- θ) + 1)

4 csc (2 θ) + 8 = 0

tan (x) = - \frac{4}{7}