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受欢迎的三角函数 >

tan(x)=2cos(x)tan(x)

解答

tan (x) = 2 cos (x) tan (x)

解答

x = πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

求解步骤

tan (x) = 2 cos (x) tan (x)

两边减去

2 cos (x) tan (x)

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

分解

tan (x) - 2 cos (x) tan (x) : - tan (x) (2 cos (x) - 1)

tan (x) - 2 cos (x) tan (x)

因式分解出通项

- tan (x)

= - tan (x) (- 1 + 2 cos (x))

- tan (x) (2 cos (x) - 1) = 0

分别求解每个部分

tan (x) = 0 or 2 cos (x) - 1 = 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

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 cos (x) - 1 = 0

将

1

到右边

2 cos (x) - 1 = 0

两边加上

1

2 cos (x) - 1 + 1 = 0 + 1

化简

2 cos (x) = 1

2 cos (x) = 1

两边除以

2

2 cos (x) = 1

两边除以

2

\frac{2 cos ( x )}{2} = \frac{1}{2}

化简

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

的通解

cos (x)

周期表（周期为

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

合并所有解

x = πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

作图

流行的例子

tan (θ) = 2.6

2sin^2(x)=1+cos(x)

2 sin^{2} (x) = 1 + cos (x)

sin (θ) = \frac{8}{17}

cos^2(x)-3sin(x)=3

cos^{2} (x) - 3 sin (x) = 3

7sin(x)cos(x)=8cos(x)

7 sin (x) cos (x) = 8 cos (x)