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受欢迎的三角函数 >

6cos(2x)+8sin(2x)=0

解答

6 cos (2 x) + 8 sin (2 x) = 0

解答

x = - \frac{0.64350 \dots}{2} + \frac{πn}{2}

+1

度数

x = - 18.43494 \dots^{\circ} + 9 0^{\circ} n

求解步骤

6 cos (2 x) + 8 sin (2 x) = 0

使用三角恒等式改写

6 cos (2 x) + 8 sin (2 x) = 0

在两边除以

cos (2 x), cos (2 x) \neq = 0

\frac{6 cos ( 2 x ) + 8 sin ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

化简

6 + \frac{8 sin ( 2 x )}{cos ( 2 x )} = 0

使用基本三角恒等式:

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

6 + 8 tan (2 x) = 0

6 + 8 tan (2 x) = 0

将

6

到右边

6 + 8 tan (2 x) = 0

两边减去

6

6 + 8 tan (2 x) - 6 = 0 - 6

化简

8 tan (2 x) = - 6

8 tan (2 x) = - 6

两边除以

8

8 tan (2 x) = - 6

两边除以

8

\frac{8 tan ( 2 x )}{8} = \frac{- 6}{8}

化简

\frac{8 tan ( 2 x )}{8} = \frac{- 6}{8}

化简

\frac{8 tan ( 2 x )}{8} : tan (2 x)

\frac{8 tan ( 2 x )}{8}

数字相除:

\frac{8}{8} = 1

= tan (2 x)

化简

\frac{- 6}{8} : - \frac{3}{4}

\frac{- 6}{8}

使用分式法则:

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

= - \frac{6}{8}

约分:

2

= - \frac{3}{4}

tan (2 x) = - \frac{3}{4}

tan (2 x) = - \frac{3}{4}

tan (2 x) = - \frac{3}{4}

使用反三角函数性质

tan (2 x) = - \frac{3}{4}

tan (2 x) = - \frac{3}{4}

的通解

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

2 x = arctan (- \frac{3}{4}) + πn

2 x = arctan (- \frac{3}{4}) + πn

解

2 x = arctan (- \frac{3}{4}) + πn : x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

2 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

2 x = - arctan (\frac{3}{4}) + πn

两边除以

2

2 x = - arctan (\frac{3}{4}) + πn

两边除以

2

\frac{2 x}{2} = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

化简

x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

以小数形式表示解

x = - \frac{0.64350 \dots}{2} + \frac{πn}{2}

作图

流行的例子

cos(x)= 8/17 ,sin(x)

cos (x) = \frac{8}{17}, sin (x)

(50)/(sin(105))=(20)/(sin(x))

\frac{50}{sin ( 10 5 ^{\circ} )} = \frac{20}{sin ( x )}

csc (θ) = - 1.343

csc(θ)=-3/2 ,pi<θ<(3pi)/2 ,sin(θ)

csc (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}, sin (θ)

sin (2 x) = \frac{- 3}{2}