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受欢迎的三角函数 >

4sin(β)+2=3+2sin(β)

解答

4 sin (β) + 2 = 3 + 2 sin (β)

解答

β = \frac{π}{6} + 2 πn, β = \frac{5 π}{6} + 2 πn

+1

度数

β = 3 0^{\circ} + 36 0^{\circ} n, β = 15 0^{\circ} + 36 0^{\circ} n

求解步骤

4 sin (β) + 2 = 3 + 2 sin (β)

用替代法求解

4 sin (β) + 2 = 3 + 2 sin (β)

令

: sin (β) = u

4 u + 2 = 3 + 2 u

4 u + 2 = 3 + 2 u : u = \frac{1}{2}

4 u + 2 = 3 + 2 u

将

2

到右边

4 u + 2 = 3 + 2 u

两边减去

2

4 u + 2 - 2 = 3 + 2 u - 2

化简

4 u = 2 u + 1

4 u = 2 u + 1

将

2 u

para o lado esquerdo

4 u = 2 u + 1

两边减去

2 u

4 u - 2 u = 2 u + 1 - 2 u

化简

2 u = 1

2 u = 1

两边除以

2

2 u = 1

两边除以

2

\frac{2 u}{2} = \frac{1}{2}

化简

u = \frac{1}{2}

u = \frac{1}{2}

u = sin (β)

代回

sin (β) = \frac{1}{2}

sin (β) = \frac{1}{2}

sin (β) = \frac{1}{2} : β = \frac{π}{6} + 2 πn, β = \frac{5 π}{6} + 2 πn

sin (β) = \frac{1}{2}

sin (β) = \frac{1}{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}

β = \frac{π}{6} + 2 πn, β = \frac{5 π}{6} + 2 πn

β = \frac{π}{6} + 2 πn, β = \frac{5 π}{6} + 2 πn

合并所有解

β = \frac{π}{6} + 2 πn, β = \frac{5 π}{6} + 2 πn

作图

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