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受欢迎的三角函数 >

-sin(x)(2+sin(x))-cos^2(x)=0

解答

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

解答

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度数

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

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

使用三角恒等式改写

- cos^{2} (x) - (2 + sin (x)) sin (x)

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= - (1 - sin^{2} (x)) - (2 + sin (x)) sin (x)

化简

- (1 - sin^{2} (x)) - (2 + sin (x)) sin (x) : - 2 sin (x) - 1

- (1 - sin^{2} (x)) - (2 + sin (x)) sin (x)

= - (1 - sin^{2} (x)) - sin (x) (2 + sin (x))

- (1 - sin^{2} (x)) : - 1 + sin^{2} (x)

- (1 - sin^{2} (x))

打开括号

= - (1) - (- sin^{2} (x))

使用加减运算法则

- (- a) = a, - (a) = - a

= - 1 + sin^{2} (x)

= - 1 + sin^{2} (x) - (2 + sin (x)) sin (x)

乘开

- sin (x) (2 + sin (x)) : - 2 sin (x) - sin^{2} (x)

- sin (x) (2 + sin (x))

使用分配律:

a (b + c) = ab + a c

a = - sin (x), b = 2, c = sin (x)

= - sin (x) \cdot 2 + (- sin (x)) sin (x)

使用加减运算法则

+ (- a) = - a

= - 2 sin (x) - sin (x) sin (x)

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

sin (x) sin (x)

使用指数法则:

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

sin (x) sin (x) = sin^{1 + 1} (x)

= sin^{1 + 1} (x)

数字相加:

1 + 1 = 2

= sin^{2} (x)

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

= - 1 + sin^{2} (x) - 2 sin (x) - sin^{2} (x)

化简

- 1 + sin^{2} (x) - 2 sin (x) - sin^{2} (x) : - 2 sin (x) - 1

- 1 + sin^{2} (x) - 2 sin (x) - sin^{2} (x)

对同类项分组

= sin^{2} (x) - 2 sin (x) - sin^{2} (x) - 1

同类项相加:

sin^{2} (x) - sin^{2} (x) = 0

= - 2 sin (x) - 1

= - 2 sin (x) - 1

= - 2 sin (x) - 1

- 1 - 2 sin (x) = 0

将

1

到右边

- 1 - 2 sin (x) = 0

两边加上

1

- 1 - 2 sin (x) + 1 = 0 + 1

化简

- 2 sin (x) = 1

- 2 sin (x) = 1

两边除以

- 2

- 2 sin (x) = 1

两边除以

- 2

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

化简

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

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

sin (x) = - \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}

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

作图

流行的例子

cos (b) = 0.3125

sin (\frac{1}{2} x) - 1 = 0

-1/16 sin(x/4)=0

- \frac{1}{16} sin (\frac{x}{4}) = 0

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

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

solvefor x,sin(x-y)=0

so l v e f or x, sin (x - y) = 0