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受欢迎的三角函数 >

(4+tan(x))(3sin(x)-2)=0

解答

(4 + tan (x)) (3 sin (x) - 2) = 0

解答

x = - 1.32581 \dots + πn, x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

+1

度数

x = - 75.96375 \dots^{\circ} + 18 0^{\circ} n, x = 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 138.18968 \dots^{\circ} + 36 0^{\circ} n

求解步骤

(4 + tan (x)) (3 sin (x) - 2) = 0

分别求解每个部分

4 + tan (x) = 0 or 3 sin (x) - 2 = 0

4 + tan (x) = 0 : x = arctan (- 4) + πn

4 + tan (x) = 0

将

4

到右边

4 + tan (x) = 0

两边减去

4

4 + tan (x) - 4 = 0 - 4

化简

tan (x) = - 4

tan (x) = - 4

使用反三角函数性质

tan (x) = - 4

tan (x) = - 4

的通解

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

x = arctan (- 4) + πn

x = arctan (- 4) + πn

3 sin (x) - 2 = 0 : x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

3 sin (x) - 2 = 0

将

2

到右边

3 sin (x) - 2 = 0

两边加上

2

3 sin (x) - 2 + 2 = 0 + 2

化简

3 sin (x) = 2

3 sin (x) = 2

两边除以

3

3 sin (x) = 2

两边除以

3

\frac{3 sin ( x )}{3} = \frac{2}{3}

化简

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

使用反三角函数性质

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

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

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

合并所有解

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

以小数形式表示解

x = - 1.32581 \dots + πn, x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

作图

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