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受欢迎的三角函数 >

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

解答

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

解答

x = πn

+1

度数

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

求解步骤

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

两边减去

cos^{2} (x)

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

使用三角恒等式改写

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

使用毕达哥拉斯恒等式:

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

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

= cos (2 x) - 1

cos (2 x) - 1 = 0

将

1

到右边

cos (2 x) - 1 = 0

两边加上

1

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

化简

cos (2 x) = 1

cos (2 x) = 1

cos (2 x) = 1

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 x = 0 + 2 πn

2 x = 0 + 2 πn

解

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

两边除以

2

2 x = 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 πn}{2}

化简

x = πn

x = πn

x = πn

作图

流行的例子

cos (x) = 0, 56

cos (\frac{x}{2}) = \frac{5}{6}

sin (B) = \frac{9}{16}

(sin(118))/(18.03)=(sin(b))/(17)

\frac{sin ( 11 8 ^{\circ} )}{18.03} = \frac{sin ( b ^{\circ} )}{17}

45=57.7+arctan((3.5)/x)-arctan((175)/x)

4 5^{\circ} = 57. 7^{\circ} + arctan (\frac{3.5}{x}) - arctan (\frac{175}{x})