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受欢迎的三角函数 >

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

解答

3 cos (x) csc (x) = 23 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) = 23 cos (x)

两边减去

23 cos (x)

3 cos (x) csc (x) - 23 cos (x) = 0

分解

3 cos (x) csc (x) - 23 cos (x) : cos (x) (3 csc (x) - 23)

3 cos (x) csc (x) - 23 cos (x)

因式分解出通项

cos (x)

= cos (x) (3 csc (x) - 23)

cos (x) (3 csc (x) - 23) = 0

分别求解每个部分

cos (x) = 0 or 3 csc (x) - 23 = 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) - 23 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

3 csc (x) - 23 = 0

将

23

到右边

3 csc (x) - 23 = 0

两边加上

23

3 csc (x) - 23 + 23 = 0 + 23

化简

3 csc (x) = 23

3 csc (x) = 23

两边除以

3

3 csc (x) = 23

两边除以

3

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

化简

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

cos (2 x) = \frac{9}{41}

sec(5x)= 2/(sqrt(3))

sec (5 x) = \frac{2}{3}

cos(a)=-4/9 , pi/2 <= a<= pi

cos (a) = - \frac{4}{9}, \frac{π}{2} \leq a \leq π

20sin^2(x)-26sin(x)+8=0

20 sin^{2} (x) - 26 sin (x) + 8 = 0

1.5=1+0.6cos((pit)/2)

1.5 = 1 + 0.6 cos (\frac{π t}{2})