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受欢迎的三角函数 >

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

解答

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

解答

x = 2 πn, x = π + 2 πn

+1

度数

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

求解步骤

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

用替代法求解

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

令

: sin (x) = u

2 u^{2} = 3 u

2 u^{2} = 3 u : u = 0, u = \frac{3}{2}

2 u^{2} = 3 u

将

3 u

para o lado esquerdo

2 u^{2} = 3 u

两边减去

3 u

2 u^{2} - 3 u = 3 u - 3 u

化简

2 u^{2} - 3 u = 0

2 u^{2} - 3 u = 0

因式分解

2 u^{2} - 3 u : u (2 u - 3)

2 u^{2} - 3 u

使用指数法则:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= 2 uu - 3 u

因式分解出通项

u

= u (2 u - 3)

u (2 u - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

u = 0 or 2 u - 3 = 0

解

2 u - 3 = 0 : u = \frac{3}{2}

2 u - 3 = 0

将

3

到右边

2 u - 3 = 0

两边加上

3

2 u - 3 + 3 = 0 + 3

化简

2 u = 3

2 u = 3

两边除以

2

2 u = 3

两边除以

2

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

化简

u = \frac{3}{2}

u = \frac{3}{2}

二次方程组的解是:

u = 0, u = \frac{3}{2}

u = sin (x)

代回

sin (x) = 0, sin (x) = \frac{3}{2}

sin (x) = 0, sin (x) = \frac{3}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

sin (x) = 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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

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

无解

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

- 1 \leq sin (x) \leq 1

无解

合并所有解

x = 2 πn, x = π + 2 πn

作图

流行的例子

5 + 2 sin (x) - 7 = 0

0.5 = 1 - sin (θ)

solvefor θ,r=6sin(2θ)

so l v e f or θ, r = 6 sin (2 θ)

1.5sin(30)=sin(x)

1.5 sin (3 0^{\circ}) = sin (x)

sqrt(3)sin(x)-3cos(x)=sqrt(6)

3 sin (x) - 3 cos (x) = 6