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受欢迎的三角函数 >

7cos(x)tan(x)-5tan(x)=0

解答

7 cos (x) tan (x) - 5 tan (x) = 0

解答

x = πn, x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 44.41530 \dots^{\circ} + 36 0^{\circ} n, x = 315.58469 \dots^{\circ} + 36 0^{\circ} n

求解步骤

7 cos (x) tan (x) - 5 tan (x) = 0

分解

7 cos (x) tan (x) - 5 tan (x) : tan (x) (7 cos (x) - 5)

7 cos (x) tan (x) - 5 tan (x)

因式分解出通项

tan (x)

= tan (x) (7 cos (x) - 5)

tan (x) (7 cos (x) - 5) = 0

分别求解每个部分

tan (x) = 0 or 7 cos (x) - 5 = 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

7 cos (x) - 5 = 0 : x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

7 cos (x) - 5 = 0

将

5

到右边

7 cos (x) - 5 = 0

两边加上

5

7 cos (x) - 5 + 5 = 0 + 5

化简

7 cos (x) = 5

7 cos (x) = 5

两边除以

7

7 cos (x) = 5

两边除以

7

\frac{7 cos ( x )}{7} = \frac{5}{7}

化简

cos (x) = \frac{5}{7}

cos (x) = \frac{5}{7}

使用反三角函数性质

cos (x) = \frac{5}{7}

cos (x) = \frac{5}{7}

的通解

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

x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

合并所有解

x = πn, x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

以小数形式表示解

x = πn, x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

作图

流行的例子

sec^2(x)-6sec(x)=0

sec^{2} (x) - 6 sec (x) = 0

9sec^2(x)tan(x)=12tan(x)

9 sec^{2} (x) tan (x) = 12 tan (x)

cos (x) = - \frac{4}{7}

(8cos(θ)-4)(5sin(θ)-5)=0

(8 cos (θ) - 4) (5 sin (θ) - 5) = 0

arctan(x)= pi/3

arctan (x) = \frac{π}{3}