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受欢迎的三角函数 >

6sin(a)+4=2sin(a)+8

解答

6 sin (a) + 4 = 2 sin (a) + 8

解答

a = \frac{π}{2} + 2 πn

+1

度数

a = 9 0^{\circ} + 36 0^{\circ} n

求解步骤

6 sin (a) + 4 = 2 sin (a) + 8

用替代法求解

6 sin (a) + 4 = 2 sin (a) + 8

令

: sin (a) = u

6 u + 4 = 2 u + 8

6 u + 4 = 2 u + 8 : u = 1

6 u + 4 = 2 u + 8

将

4

到右边

6 u + 4 = 2 u + 8

两边减去

4

6 u + 4 - 4 = 2 u + 8 - 4

化简

6 u = 2 u + 4

6 u = 2 u + 4

将

2 u

para o lado esquerdo

6 u = 2 u + 4

两边减去

2 u

6 u - 2 u = 2 u + 4 - 2 u

化简

4 u = 4

4 u = 4

两边除以

4

4 u = 4

两边除以

4

\frac{4 u}{4} = \frac{4}{4}

化简

u = 1

u = 1

u = sin (a)

代回

sin (a) = 1

sin (a) = 1

sin (a) = 1 : a = \frac{π}{2} + 2 πn

sin (a) = 1

sin (a) = 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}

a = \frac{π}{2} + 2 πn

a = \frac{π}{2} + 2 πn

合并所有解

a = \frac{π}{2} + 2 πn

作图

流行的例子

sin(3x)=0,-2<x<2

sin (3 x) = 0, - 2 < x < 2

tan (x) = \frac{2}{6}

2sin^2(x)-5sin(x)=3

2 sin^{2} (x) - 5 sin (x) = 3

cos(8x)-cos(2x)=sin(5x)

cos (8 x) - cos (2 x) = sin (5 x)

tan (x) = - \frac{1}{5}