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受欢迎的三角函数 >

20/3 sin(10x)+5cos(10x)=0

解答

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

解答

x = - \frac{0.64350 \dots}{10} + \frac{πn}{10}

+1

度数

x = - 3.68698 \dots^{\circ} + 1 8^{\circ} n

求解步骤

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

使用三角恒等式改写

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

在两边除以

cos (10 x), cos (10 x) \neq = 0

\frac{\frac{20}{3} sin ( 10 x ) + 5 cos ( 10 x )}{cos ( 10 x )} = \frac{0}{cos ( 10 x )}

化简

\frac{20 sin ( 10 x )}{3 cos ( 10 x )} + 5 = 0

使用基本三角恒等式:

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

\frac{20 tan ( 10 x )}{3} + 5 = 0

\frac{20 tan ( 10 x )}{3} + 5 = 0

将

5

到右边

\frac{20 tan ( 10 x )}{3} + 5 = 0

两边减去

5

\frac{20 tan ( 10 x )}{3} + 5 - 5 = 0 - 5

化简

\frac{20 tan ( 10 x )}{3} = - 5

\frac{20 tan ( 10 x )}{3} = - 5

在两边乘以

3

\frac{20 tan ( 10 x )}{3} = - 5

在两边乘以

3

\frac{3 \cdot 20 tan ( 10 x )}{3} = 3 (- 5)

化简

20 tan (10 x) = - 15

20 tan (10 x) = - 15

两边除以

20

20 tan (10 x) = - 15

两边除以

20

\frac{20 tan ( 10 x )}{20} = \frac{- 15}{20}

化简

\frac{20 tan ( 10 x )}{20} = \frac{- 15}{20}

化简

\frac{20 tan ( 10 x )}{20} : tan (10 x)

\frac{20 tan ( 10 x )}{20}

数字相除:

\frac{20}{20} = 1

= tan (10 x)

化简

\frac{- 15}{20} : - \frac{3}{4}

\frac{- 15}{20}

使用分式法则:

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

= - \frac{15}{20}

约分:

5

= - \frac{3}{4}

tan (10 x) = - \frac{3}{4}

tan (10 x) = - \frac{3}{4}

tan (10 x) = - \frac{3}{4}

使用反三角函数性质

tan (10 x) = - \frac{3}{4}

tan (10 x) = - \frac{3}{4}

的通解

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

10 x = arctan (- \frac{3}{4}) + πn

10 x = arctan (- \frac{3}{4}) + πn

解

10 x = arctan (- \frac{3}{4}) + πn : x = - \frac{arctan ( \frac{3}{4} )}{10} + \frac{πn}{10}

10 x = arctan (- \frac{3}{4}) + πn

化简

arctan (- \frac{3}{4}) + πn : - arctan (\frac{3}{4}) + πn

arctan (- \frac{3}{4}) + πn

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{4}) = - arctan (\frac{3}{4})

= - arctan (\frac{3}{4}) + πn

10 x = - arctan (\frac{3}{4}) + πn

两边除以

10

10 x = - arctan (\frac{3}{4}) + πn

两边除以

10

\frac{10 x}{10} = - \frac{arctan ( \frac{3}{4} )}{10} + \frac{πn}{10}

化简

x = - \frac{arctan ( \frac{3}{4} )}{10} + \frac{πn}{10}

x = - \frac{arctan ( \frac{3}{4} )}{10} + \frac{πn}{10}

x = - \frac{arctan ( \frac{3}{4} )}{10} + \frac{πn}{10}

以小数形式表示解

x = - \frac{0.64350 \dots}{10} + \frac{πn}{10}

作图

流行的例子

cos(3x+pi/4)=-(sqrt(3))/2

cos (3 x + \frac{π}{4}) = - \frac{3}{2}

sin (x) - \frac{1}{4} = 0

sqrt(2)csc(θ)-2=0

2 csc (θ) - 2 = 0

sin(θ)=(sqrt(5))/4

sin (θ) = \frac{5}{4}

100=50sqrt(40)cos(θ)

100 = 5040 cos (θ)