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受欢迎的三角函数 >

9sin(x)tan(x)=-4tan(x)

解答

9 sin (x) tan (x) = - 4 tan (x)

解答

x = πn, x = - 0.46055 \dots + 2 πn, x = π + 0.46055 \dots + 2 πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = - 26.38779 \dots^{\circ} + 36 0^{\circ} n, x = 206.38779 \dots^{\circ} + 36 0^{\circ} n

求解步骤

9 sin (x) tan (x) = - 4 tan (x)

两边减去

- 4 tan (x)

9 sin (x) tan (x) + 4 tan (x) = 0

分解

9 sin (x) tan (x) + 4 tan (x) : tan (x) (9 sin (x) + 4)

9 sin (x) tan (x) + 4 tan (x)

因式分解出通项

tan (x)

= tan (x) (9 sin (x) + 4)

tan (x) (9 sin (x) + 4) = 0

分别求解每个部分

tan (x) = 0 or 9 sin (x) + 4 = 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

9 sin (x) + 4 = 0 : x = arcsin (- \frac{4}{9}) + 2 πn, x = π + arcsin (\frac{4}{9}) + 2 πn

9 sin (x) + 4 = 0

将

4

到右边

9 sin (x) + 4 = 0

两边减去

4

9 sin (x) + 4 - 4 = 0 - 4

化简

9 sin (x) = - 4

9 sin (x) = - 4

两边除以

9

9 sin (x) = - 4

两边除以

9

\frac{9 sin ( x )}{9} = \frac{- 4}{9}

化简

sin (x) = - \frac{4}{9}

sin (x) = - \frac{4}{9}

使用反三角函数性质

sin (x) = - \frac{4}{9}

sin (x) = - \frac{4}{9}

的通解

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

x = arcsin (- \frac{4}{9}) + 2 πn, x = π + arcsin (\frac{4}{9}) + 2 πn

x = arcsin (- \frac{4}{9}) + 2 πn, x = π + arcsin (\frac{4}{9}) + 2 πn

合并所有解

x = πn, x = arcsin (- \frac{4}{9}) + 2 πn, x = π + arcsin (\frac{4}{9}) + 2 πn

以小数形式表示解

x = πn, x = - 0.46055 \dots + 2 πn, x = π + 0.46055 \dots + 2 πn

作图

流行的例子

tan^2(θ)-3tan(θ)=0

tan^{2} (θ) - 3 tan (θ) = 0

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

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

2cos^2(x)+3cos(x)=0

2 cos^{2} (x) + 3 cos (x) = 0

solvefor y,sin(y)=x

so l v e f or y, sin (y) = x

sin(2x)+sqrt(3)cos(x)=0

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