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受欢迎的三角函数 >

2cos^2(x)-sqrt(3)*sin^2(x)-2=0

解答

2 cos^{2} (x) - 3 \cdot sin^{2} (x) - 2 = 0

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

使用三角恒等式改写

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

使用毕达哥拉斯恒等式:

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

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

= - 2 + 2 (1 - sin^{2} (x)) - sin^{2} (x) 3

化简

- 2 + 2 (1 - sin^{2} (x)) - sin^{2} (x) 3 : - 2 sin^{2} (x) - 3 sin^{2} (x)

- 2 + 2 (1 - sin^{2} (x)) - sin^{2} (x) 3

= - 2 + 2 (1 - sin^{2} (x)) - 3 sin^{2} (x)

乘开

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

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

使用分配律:

a (b - c) = ab - a c

a = 2, b = 1, c = sin^{2} (x)

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

数字相乘:

2 \cdot 1 = 2

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

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

- 2 + 2 = 0

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

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

- 2 sin^{2} (x) - sin^{2} (x) 3 = 0

用替代法求解

- 2 sin^{2} (x) - sin^{2} (x) 3 = 0

令

: sin (x) = u

- 2 u^{2} - u^{2} 3 = 0

- 2 u^{2} - u^{2} 3 = 0 : u = 0

- 2 u^{2} - u^{2} 3 = 0

分解

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

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

因式分解出通项

u^{2}

= - u^{2} (2 + 3)

- (2 + 3) u^{2} = 0

两边除以

- 2 - 3

- (2 + 3) u^{2} = 0

两边除以

- 2 - 3

- (2 + 3) u^{2} = 0

两边除以

- 2 - 3

\frac{- ( 2 + 3 ) u ^{2}}{- 2 - 3} = \frac{0}{- 2 - 3}

化简

u^{2} = 0

u^{2} = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

u = 0

u = sin (x)

代回

sin (x) = 0

sin (x) = 0

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

合并所有解

x = 2 πn, x = π + 2 πn

作图

流行的例子

solvefor x,log_{10}(y)=arctan(x)+c

so l v e f or x, lo g_{10} (y) = arctan (x) + c

2sin(x)=((4sin(x)-cos(x)))/2

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

cos(x+60)*cos(x-60)= 1/2

cos (x + 60) \cdot cos (x - 60) = \frac{1}{2}

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\frac{cos ( 2 x + 9 )}{3} = \frac{1}{2}

sin^6(x)-cos^6(x)=0

sin^{6} (x) - cos^{6} (x) = 0