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受欢迎的三角函数 >

8sin(b)+1=sin(b)+1

解答

8 sin (b) + 1 = sin (b) + 1

解答

b = 2 πn, b = π + 2 πn

+1

度数

b = 0^{\circ} + 36 0^{\circ} n, b = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

8 sin (b) + 1 = sin (b) + 1

用替代法求解

8 sin (b) + 1 = sin (b) + 1

令

: sin (b) = u

8 u + 1 = u + 1

8 u + 1 = u + 1 : u = 0

8 u + 1 = u + 1

两边减去

1

8 u + 1 - 1 = u + 1 - 1

化简

8 u = u

将

u

para o lado esquerdo

8 u = u

两边减去

u

8 u - u = u - u

化简

7 u = 0

7 u = 0

两边除以

7

7 u = 0

两边除以

7

\frac{7 u}{7} = \frac{0}{7}

化简

u = 0

u = 0

u = sin (b)

代回

sin (b) = 0

sin (b) = 0

sin (b) = 0 : b = 2 πn, b = π + 2 πn

sin (b) = 0

sin (b) = 0

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}

b = 0 + 2 πn, b = π + 2 πn

b = 0 + 2 πn, b = π + 2 πn

解

b = 0 + 2 πn : b = 2 πn

b = 0 + 2 πn

0 + 2 πn = 2 πn

b = 2 πn

b = 2 πn, b = π + 2 πn

合并所有解

b = 2 πn, b = π + 2 πn

作图

流行的例子

7 cos (3 x) = 7

sin(x+pi/4)+sin(x-pi/4)-1=0

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) - 1 = 0

1/2 sin(x)=-(sqrt(3))/4

\frac{1}{2} sin (x) = - \frac{3}{4}

cos^2(x)+3cos(x)-4=0

cos^{2} (x) + 3 cos (x) - 4 = 0

7sin(x)=cos(x)-3

7 sin (x) = cos (x) - 3