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受欢迎的三角函数 >

solvefor a,sin^2(a)+cos^2(b)=1

解答

求解

a, sin^{2} (a) + cos^{2} (b) = 1

解答

a = arcsin (- sin (b)) + 2 πn, a = π + arcsin (sin (b)) + 2 πn, a = arcsin (sin (b)) + 2 πn, a = π + arcsin (- sin (b)) + 2 πn

求解步骤

sin^{2} (a) + cos^{2} (b) = 1

两边减去

1

sin^{2} (a) + cos^{2} (b) - 1 = 0

使用三角恒等式改写

- 1 + cos^{2} (b) + sin^{2} (a)

使用毕达哥拉斯恒等式:

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

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

= sin^{2} (a) - sin^{2} (b)

- sin^{2} (b) + sin^{2} (a) = 0

分解

- sin^{2} (b) + sin^{2} (a) : (sin (a) + sin (b)) (sin (a) - sin (b))

- sin^{2} (b) + sin^{2} (a)

使用平方差公式:

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

sin^{2} (a) - sin^{2} (b) = (sin (a) + sin (b)) (sin (a) - sin (b))

= (sin (a) + sin (b)) (sin (a) - sin (b))

(sin (a) + sin (b)) (sin (a) - sin (b)) = 0

分别求解每个部分

sin (a) + sin (b) = 0 or sin (a) - sin (b) = 0

sin (a) + sin (b) = 0 : a = arcsin (- sin (b)) + 2 πn, a = π + arcsin (sin (b)) + 2 πn

sin (a) + sin (b) = 0

将

sin (b)

到右边

sin (a) + sin (b) = 0

两边减去

sin (b)

sin (a) + sin (b) - sin (b) = 0 - sin (b)

化简

sin (a) = - sin (b)

sin (a) = - sin (b)

使用反三角函数性质

sin (a) = - sin (b)

sin (a) = - sin (b)

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

a = arcsin (- sin (b)) + 2 πn, a = π + arcsin (sin (b)) + 2 πn

a = arcsin (- sin (b)) + 2 πn, a = π + arcsin (sin (b)) + 2 πn

sin (a) - sin (b) = 0 : a = arcsin (sin (b)) + 2 πn, a = π + arcsin (- sin (b)) + 2 πn

sin (a) - sin (b) = 0

将

sin (b)

到右边

sin (a) - sin (b) = 0

两边加上

sin (b)

sin (a) - sin (b) + sin (b) = 0 + sin (b)

化简

sin (a) = sin (b)

sin (a) = sin (b)

使用反三角函数性质

sin (a) = sin (b)

sin (a) = sin (b)

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

a = arcsin (sin (b)) + 2 πn, a = π + arcsin (- sin (b)) + 2 πn

a = arcsin (sin (b)) + 2 πn, a = π + arcsin (- sin (b)) + 2 πn

合并所有解

a = arcsin (- sin (b)) + 2 πn, a = π + arcsin (sin (b)) + 2 πn, a = arcsin (sin (b)) + 2 πn, a = π + arcsin (- sin (b)) + 2 πn

作图

流行的例子

sin^4(x)=-cos(x)

sin^{4} (x) = - cos (x)

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cos^{3} (x) = 4 cos^{3} (x) - 3 cos (x)

4sin^4(x)+12cos^2(x)-7=0

4 sin^{4} (x) + 12 cos^{2} (x) - 7 = 0

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