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受欢迎的三角函数 >

3cos(3x)-15sin(3x)=0

解答

3 cos (3 x) - 15 sin (3 x) = 0

解答

x = \frac{0.19739 \dots}{3} + \frac{πn}{3}

+1

度数

x = 3.76997 \dots^{\circ} + 6 0^{\circ} n

求解步骤

3 cos (3 x) - 15 sin (3 x) = 0

使用三角恒等式改写

3 cos (3 x) - 15 sin (3 x) = 0

在两边除以

cos (3 x), cos (3 x) \neq = 0

\frac{3 cos ( 3 x ) - 15 sin ( 3 x )}{cos ( 3 x )} = \frac{0}{cos ( 3 x )}

化简

3 - \frac{15 sin ( 3 x )}{cos ( 3 x )} = 0

使用基本三角恒等式:

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

3 - 15 tan (3 x) = 0

3 - 15 tan (3 x) = 0

将

3

到右边

3 - 15 tan (3 x) = 0

两边减去

3

3 - 15 tan (3 x) - 3 = 0 - 3

化简

- 15 tan (3 x) = - 3

- 15 tan (3 x) = - 3

两边除以

- 15

- 15 tan (3 x) = - 3

两边除以

- 15

\frac{- 15 tan ( 3 x )}{- 15} = \frac{- 3}{- 15}

化简

\frac{- 15 tan ( 3 x )}{- 15} = \frac{- 3}{- 15}

化简

\frac{- 15 tan ( 3 x )}{- 15} : tan (3 x)

\frac{- 15 tan ( 3 x )}{- 15}

使用分式法则:

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

= \frac{15 tan ( 3 x )}{15}

数字相除:

\frac{15}{15} = 1

= tan (3 x)

化简

\frac{- 3}{- 15} : \frac{1}{5}

\frac{- 3}{- 15}

使用分式法则:

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

= \frac{3}{15}

约分:

3

= \frac{1}{5}

tan (3 x) = \frac{1}{5}

tan (3 x) = \frac{1}{5}

tan (3 x) = \frac{1}{5}

使用反三角函数性质

tan (3 x) = \frac{1}{5}

tan (3 x) = \frac{1}{5}

的通解

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

3 x = arctan (\frac{1}{5}) + πn

3 x = arctan (\frac{1}{5}) + πn

解

3 x = arctan (\frac{1}{5}) + πn : x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

3 x = arctan (\frac{1}{5}) + πn

两边除以

3

3 x = arctan (\frac{1}{5}) + πn

两边除以

3

\frac{3 x}{3} = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

化简

x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

以小数形式表示解

x = \frac{0.19739 \dots}{3} + \frac{πn}{3}

作图

流行的例子

2tan(x)-3cot(x)=0

2 tan (x) - 3 cot (x) = 0

8sin(2x)+15cos(x)=0

8 sin (2 x) + 15 cos (x) = 0

cos(x/2)-2cos(x)-2=0

cos (\frac{x}{2}) - 2 cos (x) - 2 = 0

8*cos^2(3x)+6*cos(6x)=10216

8 \cdot cos^{2} (3 x) + 6 \cdot cos (6 x) = 10216

sin(x)=(48*sin(69))/(47.5)

sin (x) = \frac{48 \cdot sin ( 6 9 ^{\circ} )}{47.5}