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受欢迎的三角函数 >

(tan(x)+1)(2cos(x)-sqrt(3))=0

解答

(tan (x) + 1) (2 cos (x) - 3) = 0

解答

x = \frac{3 π}{4} + πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度数

x = 13 5^{\circ} + 18 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

(tan (x) + 1) (2 cos (x) - 3) = 0

分别求解每个部分

tan (x) + 1 = 0 or 2 cos (x) - 3 = 0

tan (x) + 1 = 0 : x = \frac{3 π}{4} + πn

tan (x) + 1 = 0

将

1

到右边

tan (x) + 1 = 0

两边减去

1

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

化简

tan (x) = - 1

tan (x) = - 1

tan (x) = - 1

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 = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

2 cos (x) - 3 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 cos (x) - 3 = 0

将

3

到右边

2 cos (x) - 3 = 0

两边加上

3

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

化简

2 cos (x) = 3

2 cos (x) = 3

两边除以

2

2 cos (x) = 3

两边除以

2

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

化简

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

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

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

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}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

合并所有解

x = \frac{3 π}{4} + πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

作图

流行的例子

sin(2x)=2cos(x)

sin (2 x) = 2 cos (x)

(sqrt(2))/2 csc(x)-1=0

\frac{2}{2} csc (x) - 1 = 0

cos(3x)cos(x)=sin(3x)sin(x)

cos (3 x) cos (x) = sin (3 x) sin (x)

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

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

2 cos (4 x) - 1 = 0