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受欢迎的三角函数 >

5/(csc(x))-5sqrt(3)cos(x)=0

解答

\frac{5}{csc ( x )} - 53 cos (x) = 0

解答

x = \frac{π}{3} + πn

+1

度数

x = 6 0^{\circ} + 18 0^{\circ} n

求解步骤

\frac{5}{csc ( x )} - 53 cos (x) = 0

化简

\frac{5}{csc ( x )} - 53 cos (x) : \frac{5 - 5 3 cos ( x ) csc ( x )}{csc ( x )}

\frac{5}{csc ( x )} - 53 cos (x)

将项转换为分式:

53 cos (x) = \frac{5 \cdot 3 cos ( x ) csc ( x )}{csc ( x )}

= \frac{5}{csc ( x )} - \frac{5 3 cos ( x ) csc ( x )}{csc ( 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{5 - 5 3 cos ( x ) csc ( x )}{csc ( x )}

\frac{5 - 5 3 cos ( x ) csc ( x )}{csc ( x )} = 0

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

5 - 53 cos (x) csc (x) = 0

使用三角恒等式改写

5 - 53 cos (x) csc (x)

csc (x) cos (x) = cot (x)

csc (x) cos (x)

用 sin, cos 表示

csc (x) cos (x)

使用基本三角恒等式:

csc (x) = \frac{1}{sin ( x )}

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

化简

\frac{1}{sin ( x )} cos (x) : \frac{cos ( x )}{sin ( x )}

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

分式相乘:

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

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

乘以:

1 \cdot cos (x) = cos (x)

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

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

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

使用基本三角恒等式:

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

= cot (x)

= 5 - 53 cot (x)

5 - 53 cot (x) = 0

将

5

到右边

5 - 53 cot (x) = 0

两边减去

5

5 - 53 cot (x) - 5 = 0 - 5

化简

- 53 cot (x) = - 5

- 53 cot (x) = - 5

两边除以

- 53

- 53 cot (x) = - 5

两边除以

- 53

\frac{- 5 3 cot ( x )}{- 5 3} = \frac{- 5}{- 5 3}

化简

\frac{- 5 3 cot ( x )}{- 5 3} = \frac{- 5}{- 5 3}

化简

\frac{- 5 3 cot ( x )}{- 5 3} : cot (x)

\frac{- 5 3 cot ( x )}{- 5 3}

使用分式法则:

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

= \frac{5 3 cot ( x )}{5 3}

数字相除:

\frac{5}{5} = 1

= \frac{3 cot ( x )}{3}

约分:

3

= cot (x)

化简

\frac{- 5}{- 5 3} : \frac{3}{3}

\frac{- 5}{- 5 3}

使用分式法则:

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

= \frac{5}{5 3}

数字相除:

\frac{5}{5} = 1

= \frac{1}{3}

\frac{1}{3}

有理化:

\frac{3}{3}

\frac{1}{3}

乘以共轭根式

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{3}{3}

= \frac{3}{3}

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

的通解

cot (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

作图

流行的例子

tan (2 y) = 1

(-6cos(x)+2sin(x))^2+32sin^2(x)=48

(- 6 cos (x) + 2 sin (x))^{2} + 32 sin^{2} (x) = 48

tan(x)csc(x)-2tan(x)=3csc(x)-6

tan (x) csc (x) - 2 tan (x) = 3 csc (x) - 6

10=7cos((pi/6)(t+6))+8

10 = 7 cos ((\frac{π}{6}) (t + 6)) + 8

cos(θ)= 1/(sqrt(6))

cos (θ) = \frac{1}{6}