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受欢迎的三角函数 >

cos^2(x)+5sin^2(x)=1

解答

cos^{2} (x) + 5 sin^{2} (x) = 1

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

cos^{2} (x) + 5 sin^{2} (x) = 1

两边减去

1

cos^{2} (x) + 5 sin^{2} (x) - 1 = 0

使用三角恒等式改写

- 1 + cos^{2} (x) + 5 sin^{2} (x)

使用毕达哥拉斯恒等式:

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

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

= 5 sin^{2} (x) - sin^{2} (x)

化简

= 4 sin^{2} (x)

4 sin^{2} (x) = 0

两边除以

4

4 sin^{2} (x) = 0

两边除以

4

4 sin^{2} (x) = 0

两边除以

4

\frac{4 sin ^{2} ( x )}{4} = \frac{0}{4}

化简

sin^{2} (x) = 0

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

-1=-4sec(y)-sec^2(y)-5

2sin^2(x)+cos(2x)=4cos^2(x)

6cos(a)+sqrt(18)=0

sin(x)+1=2cos(x)