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受欢迎的三角函数 >

tan^2(x)-sin(x)tan^2(x)=0

解答

tan^{2} (x) - sin (x) tan^{2} (x) = 0

解答

x = πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) - sin (x) tan^{2} (x) = 0

分解

tan^{2} (x) - sin (x) tan^{2} (x) : - tan^{2} (x) (sin (x) - 1)

tan^{2} (x) - sin (x) tan^{2} (x)

因式分解出通项

- tan^{2} (x)

= - tan^{2} (x) (- 1 + sin (x))

- tan^{2} (x) (sin (x) - 1) = 0

分别求解每个部分

tan^{2} (x) = 0 or sin (x) - 1 = 0

tan^{2} (x) = 0 : x = πn

tan^{2} (x) = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

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

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

sin (x) - 1 = 0

将

1

到右边

sin (x) - 1 = 0

两边加上

1

sin (x) - 1 + 1 = 0 + 1

化简

sin (x) = 1

sin (x) = 1

sin (x) = 1

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

合并所有解

x = πn, x = \frac{π}{2} + 2 πn

因为方程对以下值无定义:

\frac{π}{2} + 2 πn

x = πn

作图

流行的例子

4sin(x)=2.54648

4 sin (x) = 2.54648

5sec^3(x)-20sec(x)=0

5 sec^{3} (x) - 20 sec (x) = 0

solvefor 3cot^2(x)-1=0,x

so l v e f or 3 cot^{2} (x) - 1 = 0, x

cos(2x)-9cos(x)+5=0

cos (2 x) - 9 cos (x) + 5 = 0

cos^{2} (t) = \frac{1}{2}