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受欢迎的三角函数 >

4cos(x)tan(x)-3tan(x)=0

解答

4 cos (x) tan (x) - 3 tan (x) = 0

解答

x = πn, x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 41.40962 \dots^{\circ} + 36 0^{\circ} n, x = 318.59037 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4 cos (x) tan (x) - 3 tan (x) = 0

分解

4 cos (x) tan (x) - 3 tan (x) : tan (x) (4 cos (x) - 3)

4 cos (x) tan (x) - 3 tan (x)

因式分解出通项

tan (x)

= tan (x) (4 cos (x) - 3)

tan (x) (4 cos (x) - 3) = 0

分别求解每个部分

tan (x) = 0 or 4 cos (x) - 3 = 0

tan (x) = 0 : x = πn

tan (x) = 0

tan (x) = 0

的通解

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

4 cos (x) - 3 = 0 : x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

4 cos (x) - 3 = 0

将

3

到右边

4 cos (x) - 3 = 0

两边加上

3

4 cos (x) - 3 + 3 = 0 + 3

化简

4 cos (x) = 3

4 cos (x) = 3

两边除以

4

4 cos (x) = 3

两边除以

4

\frac{4 cos ( x )}{4} = \frac{3}{4}

化简

cos (x) = \frac{3}{4}

cos (x) = \frac{3}{4}

使用反三角函数性质

cos (x) = \frac{3}{4}

cos (x) = \frac{3}{4}

的通解

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

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

合并所有解

x = πn, x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

以小数形式表示解

x = πn, x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

作图

流行的例子

cos(x)sin(x)=2sin(x)

cos (x) sin (x) = 2 sin (x)

sin (x) = 2 cos (x)

sec (x) tan (x) = 0

2 cos (x) + 1 = 3

sec(x)+tan(x)=0

sec (x) + tan (x) = 0