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 >

sec(x)cot(x)= 7/6

解答

sec (x) cot (x) = \frac{7}{6}

解答

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

+1

度数

x = 58.99728 \dots^{\circ} + 36 0^{\circ} n, x = 121.00271 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sec (x) cot (x) = \frac{7}{6}

两边减去

\frac{7}{6}

sec (x) cot (x) - \frac{7}{6} = 0

化简

sec (x) cot (x) - \frac{7}{6} : \frac{6 sec ( x ) cot ( x ) - 7}{6}

sec (x) cot (x) - \frac{7}{6}

将项转换为分式:

sec (x) cot (x) = \frac{sec ( x ) cot ( x ) 6}{6}

= \frac{sec ( x ) cot ( x ) \cdot 6}{6} - \frac{7}{6}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{sec ( x ) cot ( x ) \cdot 6 - 7}{6}

\frac{6 sec ( x ) cot ( x ) - 7}{6} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

6 sec (x) cot (x) - 7 = 0

用 sin, cos 表示

- 7 + 6 cot (x) sec (x)

使用基本三角恒等式:

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

= - 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} sec (x)

使用基本三角恒等式:

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

= - 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

化简

- 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} : \frac{- 7 sin ( x ) + 6}{sin ( x )}

- 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} = \frac{6}{sin ( x )}

6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

分式相乘:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{cos ( x ) \cdot 1 \cdot 6}{sin ( x ) cos ( x )}

约分:

cos (x)

= \frac{1 \cdot 6}{sin ( x )}

数字相乘:

1 \cdot 6 = 6

= \frac{6}{sin ( x )}

= - 7 + \frac{6}{sin ( x )}

将项转换为分式:

7 = \frac{7 sin ( x )}{sin ( x )}

= - \frac{7 sin ( x )}{sin ( x )} + \frac{6}{sin ( x )}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 7 sin ( x ) + 6}{sin ( x )}

= \frac{- 7 sin ( x ) + 6}{sin ( x )}

\frac{6 - 7 sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

6 - 7 sin (x) = 0

将

6

到右边

6 - 7 sin (x) = 0

两边减去

6

6 - 7 sin (x) - 6 = 0 - 6

化简

- 7 sin (x) = - 6

- 7 sin (x) = - 6

两边除以

- 7

- 7 sin (x) = - 6

两边除以

- 7

\frac{- 7 sin ( x )}{- 7} = \frac{- 6}{- 7}

化简

sin (x) = \frac{6}{7}

sin (x) = \frac{6}{7}

使用反三角函数性质

sin (x) = \frac{6}{7}

sin (x) = \frac{6}{7}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

以小数形式表示解

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

作图

流行的例子

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

sin^{2} (x) - 3 sin (x) cos (x) + 2 cos^{2} (x) = 0

sin(t)=-(sqrt(2))/2

sin (t) = - \frac{2}{2}

9cos(2θ)=9cos^2(θ)-4

9 cos (2 θ) = 9 cos^{2} (θ) - 4

- 10 sin (x) = 0

sin (\frac{x}{5}) = 0