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受欢迎的三角函数 >

(tan(x)+3)(tan(x)+2)=0

解答

(tan (x) + 3) (tan (x) + 2) = 0

解答

x = - 1.24904 \dots + πn, x = - 1.10714 \dots + πn

+1

度数

x = - 71.56505 \dots^{\circ} + 18 0^{\circ} n, x = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

求解步骤

(tan (x) + 3) (tan (x) + 2) = 0

分别求解每个部分

tan (x) + 3 = 0 or tan (x) + 2 = 0

tan (x) + 3 = 0 : x = arctan (- 3) + πn

tan (x) + 3 = 0

将

3

到右边

tan (x) + 3 = 0

两边减去

3

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

化简

tan (x) = - 3

tan (x) = - 3

使用反三角函数性质

tan (x) = - 3

tan (x) = - 3

的通解

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

x = arctan (- 3) + πn

x = arctan (- 3) + πn

tan (x) + 2 = 0 : x = arctan (- 2) + πn

tan (x) + 2 = 0

将

2

到右边

tan (x) + 2 = 0

两边减去

2

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

化简

tan (x) = - 2

tan (x) = - 2

使用反三角函数性质

tan (x) = - 2

tan (x) = - 2

的通解

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

x = arctan (- 2) + πn

x = arctan (- 2) + πn

合并所有解

x = arctan (- 3) + πn, x = arctan (- 2) + πn

以小数形式表示解

x = - 1.24904 \dots + πn, x = - 1.10714 \dots + πn

作图

流行的例子

2tan(θ)+sqrt(6)=0

2 tan (θ) + 6 = 0

8 = 8 cos (3 θ)

sinh (2 x) = 0

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

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

3tan(x)= 1/(cos(x))

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