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受欢迎的三角函数 >

sin^2(α)=1+cos^2(α)

解答

sin^{2} (α) = 1 + cos^{2} (α)

解答

α = \frac{π}{2} + πn

+1

度数

α = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

sin^{2} (α) = 1 + cos^{2} (α)

两边减去

1 + cos^{2} (α)

sin^{2} (α) - 1 - cos^{2} (α) = 0

使用三角恒等式改写

sin^{2} (α) - 1 - cos^{2} (α)

使用倍角公式:

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

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

= - 1 - cos (2 α)

- 1 - cos (2 α) = 0

将

1

到右边

- 1 - cos (2 α) = 0

两边加上

1

- 1 - cos (2 α) + 1 = 0 + 1

化简

- cos (2 α) = 1

- cos (2 α) = 1

两边除以

- 1

- cos (2 α) = 1

两边除以

- 1

\frac{- cos ( 2 α )}{- 1} = \frac{1}{- 1}

化简

cos (2 α) = - 1

cos (2 α) = - 1

cos (2 α) = - 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 α = π + 2 πn

2 α = π + 2 πn

解

2 α = π + 2 πn : α = \frac{π}{2} + πn

2 α = π + 2 πn

两边除以

2

2 α = π + 2 πn

两边除以

2

\frac{2 α}{2} = \frac{π}{2} + \frac{2 πn}{2}

化简

α = \frac{π}{2} + πn

α = \frac{π}{2} + πn

α = \frac{π}{2} + πn

作图

流行的例子

21cos((2pi)/(687)t)+228=220

21 cos (\frac{2 π}{687} t) + 228 = 220

cosh(npi)+sinh(npi)=0

cosh (nπ) + sinh (nπ) = 0

sin(pi/6 x)= 1/2

sin (\frac{π}{6} x) = \frac{1}{2}

cos(θ)=(sqrt(65))/(65)

cos (θ) = \frac{65}{65}

-sin(x)-sin(x+pi/3)=0

- sin (x) - sin (x + \frac{π}{3}) = 0