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受欢迎的三角函数 >

2sin(x)+(sqrt(3))/2 =sin(x)

解答

2 sin (x) + \frac{3}{2} = sin (x)

解答

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度数

x = 24 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

求解步骤

2 sin (x) + \frac{3}{2} = sin (x)

用替代法求解

2 sin (x) + \frac{3}{2} = sin (x)

令

: sin (x) = u

2 u + \frac{3}{2} = u

2 u + \frac{3}{2} = u : u = - \frac{3}{2}

2 u + \frac{3}{2} = u

将

\frac{3}{2}

到右边

2 u + \frac{3}{2} = u

两边减去

\frac{3}{2}

2 u + \frac{3}{2} - \frac{3}{2} = u - \frac{3}{2}

化简

2 u = u - \frac{3}{2}

2 u = u - \frac{3}{2}

将

u

para o lado esquerdo

2 u = u - \frac{3}{2}

两边减去

u

2 u - u = u - \frac{3}{2} - u

化简

u = - \frac{3}{2}

u = - \frac{3}{2}

u = sin (x)

代回

sin (x) = - \frac{3}{2}

sin (x) = - \frac{3}{2}

sin (x) = - \frac{3}{2} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (x) = - \frac{3}{2}

sin (x) = - \frac{3}{2}

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{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

合并所有解

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

作图

流行的例子

3tan(2x)=sqrt(3)

3 tan (2 x) = 3

12 cos^{2} (x) = 3

sqrt(2)cos(x)-sqrt(2)sin(x)=1,0<= x<2pi

2 cos (x) - 2 sin (x) = 1, 0 \leq x < 2 π

sin (x) = 3 cos (x)

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

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