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受欢迎的三角函数 >

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

解答

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

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

两边减去

2

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

使用三角恒等式改写

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

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

化简

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

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

化简

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

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

同类项相加:

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

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

- 2 + 2 = 0

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

sin^{2} (x) = 0

使用法则

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

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

作图

流行的例子

42 - 25 cos (x) = 31

2sec^2(x)=5tan(x)

2 sec^{2} (x) = 5 tan (x)

cos^2(2x)-3sin^2(x)-1=0

cos^{2} (2 x) - 3 sin^{2} (x) - 1 = 0

sin (- t) = \frac{3}{10}

cos^2(x)+sin^3(x)=0

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