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受欢迎的三角函数 >

d^2+13d+36=(sin^2(x))/2

解答

d^{2} + 13 d + 36 = \frac{sin ^{2} ( x )}{2}

解答

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

求解步骤

d^{2} + 13 d + 36 = \frac{sin ^{2} ( x )}{2}

交换两边

\frac{sin ^{2} ( x )}{2} = d^{2} + 13 d + 36

用替代法求解

\frac{sin ^{2} ( x )}{2} = d^{2} + 13 d + 36

令

: sin (x) = u

\frac{u ^{2}}{2} = d^{2} + 13 d + 36

\frac{u ^{2}}{2} = d^{2} + 13 d + 36 : u = 2 d^{2} + 26 d + 72, u = - 2 d^{2} + 26 d + 72

\frac{u ^{2}}{2} = d^{2} + 13 d + 36

在两边乘以

2

\frac{u ^{2}}{2} = d^{2} + 13 d + 36

在两边乘以

2

\frac{2 u ^{2}}{2} = 2 d^{2} + 2 \cdot 13 d + 2 \cdot 36

化简

u^{2} = 2 d^{2} + 26 d + 72

u^{2} = 2 d^{2} + 26 d + 72

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 2 d^{2} + 26 d + 72, u = - 2 d^{2} + 26 d + 72

u = sin (x)

代回

sin (x) = 2 d^{2} + 26 d + 72, sin (x) = - 2 d^{2} + 26 d + 72

sin (x) = 2 d^{2} + 26 d + 72, sin (x) = - 2 d^{2} + 26 d + 72

sin (x) = 2 d^{2} + 26 d + 72 : x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn

sin (x) = 2 d^{2} + 26 d + 72

使用反三角函数性质

sin (x) = 2 d^{2} + 26 d + 72

sin (x) = 2 d^{2} + 26 d + 72

的通解

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

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn

sin (x) = - 2 d^{2} + 26 d + 72 : x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

sin (x) = - 2 d^{2} + 26 d + 72

使用反三角函数性质

sin (x) = - 2 d^{2} + 26 d + 72

sin (x) = - 2 d^{2} + 26 d + 72

的通解

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

x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

合并所有解

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

作图

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