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 >

(sin(x))/(tan(x))=-0.375

解答

\frac{sin ( x )}{tan ( x )} = - 0.375

解答

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

+1

度数

x = 112.02431 \dots^{\circ} + 36 0^{\circ} n, x = - 112.02431 \dots^{\circ} + 36 0^{\circ} n

求解步骤

\frac{sin ( x )}{tan ( x )} = - 0.375

两边减去

- 0.375

\frac{sin ( x )}{tan ( x )} + 0.375 = 0

使用三角恒等式改写

0.375 + \frac{sin ( x )}{tan ( x )}

使用基本三角恒等式:

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

= 0.375 + \frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

\frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}} = cos (x)

\frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

使用分式法则:

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

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

约分:

sin (x)

= cos (x)

= 0.375 + cos (x)

0.375 + cos (x) = 0

将

0.375

到右边

0.375 + cos (x) = 0

两边减去

0.375

0.375 + cos (x) - 0.375 = 0 - 0.375

化简

cos (x) = - 0.375

cos (x) = - 0.375

使用反三角函数性质

cos (x) = - 0.375

cos (x) = - 0.375

的通解

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

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

以小数形式表示解

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

作图

流行的例子

4sin(x)cos(x)+5cos(x)=0

4 sin (x) cos (x) + 5 cos (x) = 0

2 sin (4 x) = 1

cos (10 x) = 0

5 + 4 cos (x) = 0

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

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