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受欢迎的三角函数 >

sqrt(3)cos(x)csc(x)=2cos(x)

解答

3 cos (x) csc (x) = 2 cos (x)

解答

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

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

求解步骤

3 cos (x) csc (x) = 2 cos (x)

两边减去

2 cos (x)

3 cos (x) csc (x) - 2 cos (x) = 0

分解

3 cos (x) csc (x) - 2 cos (x) : cos (x) (3 csc (x) - 2)

3 cos (x) csc (x) - 2 cos (x)

因式分解出通项

cos (x)

= cos (x) (3 csc (x) - 2)

cos (x) (3 csc (x) - 2) = 0

分别求解每个部分

cos (x) = 0 or 3 csc (x) - 2 = 0

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

cos (x) = 0

cos (x) = 0

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}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

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

3 csc (x) - 2 = 0

将

2

到右边

3 csc (x) - 2 = 0

两边加上

2

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

化简

3 csc (x) = 2

3 csc (x) = 2

两边除以

3

3 csc (x) = 2

两边除以

3

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

化简

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

化简

\frac{3 csc ( x )}{3} : csc (x)

\frac{3 csc ( x )}{3}

约分:

3

= csc (x)

化简

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

乘以共轭根式

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

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

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

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

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

的通解

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

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

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

合并所有解

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

作图

流行的例子

sin(2x)=-(sqrt(2))/2

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

sin(x)=0,0<= x<2pi

sin (x) = 0, 0 \leq x < 2 π

sin (z) = 100

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

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

cos (a) = \frac{3}{5}