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受欢迎的三角函数 >

solvefor y,x=cos(2y)

解答

求解

y, x = cos (2 y)

解答

y = \frac{arccos ( x )}{2} + πn, y = - \frac{arccos ( x )}{2} + πn

求解步骤

x = cos (2 y)

交换两边

cos (2 y) = x

使用反三角函数性质

cos (2 y) = x

cos (2 y) = x

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

2 y = arccos (x) + 2 πn, 2 y = - arccos (x) + 2 πn

2 y = arccos (x) + 2 πn, 2 y = - arccos (x) + 2 πn

解

2 y = arccos (x) + 2 πn : y = \frac{arccos ( x )}{2} + πn

2 y = arccos (x) + 2 πn

两边除以

2

2 y = arccos (x) + 2 πn

两边除以

2

\frac{2 y}{2} = \frac{arccos ( x )}{2} + \frac{2 πn}{2}

化简

y = \frac{arccos ( x )}{2} + πn

y = \frac{arccos ( x )}{2} + πn

解

2 y = - arccos (x) + 2 πn : y = - \frac{arccos ( x )}{2} + πn

2 y = - arccos (x) + 2 πn

两边除以

2

2 y = - arccos (x) + 2 πn

两边除以

2

\frac{2 y}{2} = - \frac{arccos ( x )}{2} + \frac{2 πn}{2}

化简

y = - \frac{arccos ( x )}{2} + πn

y = - \frac{arccos ( x )}{2} + πn

y = \frac{arccos ( x )}{2} + πn, y = - \frac{arccos ( x )}{2} + πn

作图

流行的例子

tan (x) = \frac{a}{b}

solvefor x,arcsin(3x-4y)= pi/2

so l v e f or x, arcsin (3 x - 4 y) = \frac{π}{2}

sin (x) a = \frac{π}{3}

cos(θ)= 6/(sqrt(14)*\sqrt{9)}

cos (θ) = \frac{6}{14 \cdot 9}

sin(θ+pi/4)= 1/2

sin (θ + \frac{π}{4}) = \frac{1}{2}